• Short CV
• Research interests
• Selected Publications   (download PDF files)
• Journals
• Books and Edited Volumes
• Contributions in Multiauthor Books and Proceedings
• Submitted Papers, Research Reports and Working Papers
• Coauthors
• Useful links
• Meetings and Workshops

Short CV

Born in Ravenna (Italy) on 21.08.1952.
Married to Renzo Lupini and mother of  Martino
Graduated in Mathematics cum laude in 1975 at the Bologna University (Italy)
From 1975 to 1987 researcher at ENI (Italian National Society for Energy).
From 1988 to 1992 Researcher in Mathematics for Economic Applications at the Faculty of Economics of Urbino University.
From 1992 to 1994 Associate professor in Mathematics for Economic Applications.
Since 1994 Full professor in Mathematics for Economic Applications.

Researches Interests

Dynamical Systems (stability, bifurcations and analysis of complex behaviors) and their applications to the modeling of the evolution of Economic, Financial, Social, Biological and Physical systems. The main results have been obtained in the anlysis of noninvertible maps of the plane, following the pioneering works of I. Gumowski and C. Mira. These tools have been improved and applied in the study of the dynamics in smooth models, piecewise-smooth and discontinuous ones. 

Recent research fields include:
 

• Global properties and bifurcations of attracting sets and basins of attraction in discrete time dynamical systems: homoclinic bifurcations and contact bifurcations that change the topological structure of attractors or basins of attraction.
• Dynamic properties of discrete dynamical systems and global bifurcations in iterated two-dimensional maps not defined in the whole plane due to the presence of a vanishing denominators, and related properties of focal points, prefocal curves, lobes, crescents, unbounded sets of attraction.
• Global qualitative analysis of discrete dynamical systems represented by the iteration of noninvertible maps, and study of their properties and global bifurcations by the use of critical sets. Problems of ultimate boundedness and delimitation of basins' boundaries. Applications to the description of long-run complex dynamics and problems of equilibrium selection in dynamic models for Economics, Finance and Social Sciences.
• Symmetric dynamical systems and related problems of chaos synchronization, on-off intermittency, riddling and blowout bifurcations related to the presence of Milnor attractors. Applications to dynamic symmetric games.
• Chaotic maps having an analytical solution.
• Dynamic modeling in Economic, Finance and Social Sciences: dynamic oligopoly games, models of economies with boundedly rational agents (and related problems of expectations and learning schemes) models of economies with heterogeneous agents, nonlinear models of business cycle.

SELECTED PUBLICATIONS

    Journals

L. Gardini, F. Tramontana, V. Avrutin, M. Schanz “Border Collision Bifurcations in 1D PWL map and  Leonov approach.” International Journal of Bifurcation & Chaos 2010 (to appear)    Download PDF .

 V. Avrutin, M. Schanz, L. Gardini “Calculation of bifurcation curves by map replacement” International Journal of Bifurcation & Chaos 2010 (to appear) Download PDF .

L. Gardini, F. Tramontana “Border Collision Bifurcations in 1D PWL map with one discontinuity and negative jump. Use of the first return map” International Journal of Bifurcation &             Chaos 2010 (to appear). Download PDF 

C. Mira, A. Agliari and L. Gardini “From the box-within-a-box bifurcations organization to the Julia set. Part II: Bifurcation routes to different Julia sets from an indirect embedding of a  quadratic complex map”. International Journal of Bifurcation & Chaos 2009 19(10) 1-48 Download PDF 

G.I. Bischi, L. Gardini, F. Tramontana “Bifurcation curves in discontinuous maps”, Discrete and  Continuous Dynamical Systems B,  13(2) 2010, 249-267.Download PDF 

L. Gardini, F. Tramontana, “Snap-back repellers in non smooth functions”, Regular and Chaotic Dynamics, 2010 (to appear) Download PDF

V. Avrutin, M. Schanz, L. Gardini “Self-similarity of the bandcount adding: calculation by map replacement” ”, Regular and Chaotic Dynamics, 2010 (to appear) Download PDF.

F.Tramontana, F.Westerhoff, L.Gardini “On the complicated price dynamics of a simple one-dimensional discontinuous financial market model with heterogeneous interacting traders”, Journal of Economic  Behavior and Organization (to appear) Download PDF .

I. Sushko, L. Gardini “Degenerate Bifurcations and Border Collisions in Piecewise Smooth 1D and 2D Maps”, International Journal of Bifurcation & Chaos (to appear) 2010.Download PDF 

F. Tramontana, L. Gardini, R. Dieci, F. Westerhof  “The emergence of “bull and bear” dynamics in  a nonlinear model of interacting markets”, Article ID 310471, 30 pages            doi:10.1155/2009/3104712009 Discrete Dynamical Systems in Nature and Society Download PDF .

Iryna Sushko , Laura Gardini, Tönu Puu: "Regular and Chaotic Grouwth Cyckles in a Hicksian Floor/Roof Model ", Journal of Economic Behavior and Organization, 2009 Download PDF . 

C. Mira and L. Gardini “From the box-within-a-box bifurcations organization to the Julia set. Part I: Bifurcation routes to different Julia sets from an indirect embedding of a quadratic   complex map”. International Journal of Bifurcation & Chaos 19(1) (2009) 281 – 327.Download PDF 

G.I. Bischi, L. Gardini, U. Merlone “Periodic cycles and bifurcation curves for one-dimensional  maps with two discontinuities”, Journal of Dynamical Systems and Geometric Theories, 2009    (to appear) Download PDF 

F. Tramontana, L. Gardini, P. Ferri “The dynamics of the NAIRU model with two switching regimes” Journal  of Economic Dynamic and Control Download PDF  (to appear)

V. Avrutin, M. Schanz and L. Gardini “On a special type of border-collision bifurcations occurring at infinity” (submitted) Download PDF 

G.I. Bischi, L. Gardini, U. Merlone “Impulsivity in binary choices and the emergence of periodicity”, Discrete Dynamics in Nature and Society , Article ID 407913, 22 pages,    doi:10.1155/2009/407913 (2009).      Download PDF  

Fabio Tramontana, Laura Gardini, Piero Ferri “The dynamics of the NAIRU model with two switching regimes” (submitted) Download PDF

V. Avrutin, M. Schanz and L. Gardini “Poincaré Equator collision bifurcations in piecewise smooth systems” (submitted) Download PDF

F. Tramontana, L. Gardini, G.I. Bischi “Bifurcation curves in discontinuous maps” (submitted). Download PDF

G.I. Bischi, L. Gardini, U. Merlone “Discontinuous dynamics in binary choice models with social influence”, Nonlinear Dynamics, Psychology, and Life Sciences (to appear) Download PDF

I. Sushko, L. Gardini “Center Bifurcation of a point on the Poincaré Equator”, Grazer Mathematische Berichte, 2009 (to appear) Download PDF

L. Gardini, V. Avrutin, M. Schanz “Connection between bifurcations on the Poincarè Equator and the dangerous bifurcations”, Grazer Mathematische Berichte, 2009 (to appear) Download PDF

F. Tramontana, L. Gardini “Use of homoclinic orbits and Iterated Function Systems in backward models.”  Grazer Mathematische Berichte, 2009 (to appear)Download PDF

Laura Gardini, Cars Hommes, Fabio Tramontana, Robin de Vilder “Forward and Backward Dynamics in implicitly defined Overlapping Generations Models” JEBO (to appear) Download PDF

F.Tramontana, L. Gardini, T. Puu “Duopoly games with alternative technologies”, Journal of Economic Dynamic and Control, 33, pp. 250-265, 2008. Download PDF

F. Tramontana, L. Gardini, D. Fournier-Prunaret, P. Charge “ Knot points in two-dimensional maps and related properties.”, International Journal of Bifurcation & Chaos (to appear) Download PDF

C. Mira and L. Gardini “From the box-within-a-box bifurcations organization to the Julia set. Part I: Revisited properties of the sets generated by a quadratic complex map with a real parameter”. International Journal of Bifurcation & Chaos 2009 (to appear).

L. Gardini, I.Sushko and A. Naimzada, “Growing Throwgh Chaotic Intervals”, Journal Economic Theory, Jet 143,2008, 541-557.  Downolad PDF

F.Tramontana, L. Gardini, T. Puu “Duopoly games with alternative technologies”, submitted 2007 Downolad PDF

Iryna Sushko and Laura Gardini: " Center Bifurcation for a Two-Dimensional Border-Collision Normal Form”. International Journal of Bifurcation and Chaos (to appear) 2008 Downolad PDF

L. Gardini, G.I.Bischi. C. Mira:  “Maps with Vanishing denominators” Scholarpedia article, p.16970, link: http://www.scholarpedia.org/article/Maps_with_Vanishing_Denominators.

Jose Carlos Valverde and Laura Gardini "On the changes of periodicity, in a piecewise linear  rotation model". Applied Mathematics and Computation, 2007  Downolad PDF   

C. Chiarella, R. Dieci, Laura Gardini, L. Sbragia: “Time varying confidence in a simple asset pricing  model with heterogeneous agents” Computational Economics 32 (2008) 55-72  Downolad PDF 

F. Bizzarri, M. Storace, L. Gardini “Bifurcation analysis of a circuit-related generalization of the shipmap ”, International Journal of    Bifurcation and Chaos (to appear). Downolad PDF 

A.Agliari, G.I. Bischi, R. Dieci, L. Gardini: “Homoclinic tangles associated with closed invariant curves in families of 2D maps” Grazer Math. Ber. (Proceedings ECIT04) (to appear). Downolad PDF 

G.I. Bischi, L. Gardini, C. Mira: “Basin fractalization generated by a two-dimensional family of Z1-Z3-Z1 maps” ”, International Journal of Bifurcation and Chaos (to appear) 16(3), pp.647-669, 2006. Downolad PDF 

A. Agliari, R. Dieci, L. Gardini: “Homoclinic tangles in Kaldor-like business cycle models”, Journal of Economic Behavior and Organization 62, pp, 324-347, 2007 Downolad PDF 

I. Sushko, A. Agliari, L. Gardini: “Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: border-collision bifurcation curves”, Chaos Solitons & Fractals, 29(3), pp.756-770, 2006 Downolad PDF 

T. Puu, L. Gardini, I. Sushko: “On the change of periodicities in the Hicksian multiplier-accelerator model with a consumption floor”, Chaos Solitons & Fractals. 29(3), pp.681-696, 2006. Downolad PDF 

I. Foroni, L. Gardini, X-Z He “Market mood, adaptive beliefs and asset price dynamics”, Chaos Solitons & Fractals, 29(3), pp.520-564, 2006. Downolad PDF 

C. Chiarella, R. Dieci, L. Gardini “Asset price and wealth dynamics in a financial market with heterogeneous agents”, Journal of Economic Dynamic and Control. 30, pp.1755-1786, 2006. Downolad PDF 

A.Agliari, L. Gardini, T. Puu: “Global Bifurcations in Duopoly when the Cournot Point is Destabilized via a Subcritical Neimark Bifurcation”,    International Game Theory Review. 8(1), pp.1-20, 2006. Downolad PDF 

G.I. Bischi, M. Gallegati, L. Gardini, R. Leonbruni, A. Palestrini: “Herding behaviours and non-fundamental high frequency asset price fluctuations in financial markets”, Macroeconomic Dynamics. 10, pp.502-528, 2006. Downolad PDF 

A.Agliari, C. Chiarella, L. Gardini “A Re-evaluation of the adaptive expectations in light of global nonlinear dynamic analysis”, Journal of Economic Behavior and Organization. 60, pp.526-552, 2006. Downolad PDF  

A.Agliari, L. Gardini, T. Puu: “Some global bifurcations related to the appearance of closed invariant curves”, Mathematics and Computers in Simulation, 68, pp.201-219, 2005. Downolad PDF 

I. Sushko, A. Agliari, L. Gardini: “Bistability and bifurcation curves for a unimodal piecewise smooth map ”, Discrete and Continuous Dynamical Systems, Serie B, Vol.5, N.3, pp. 881-897, 2005. Downolad PDF 

G.I. Bischi, L. Gardini, C. Mira: “Plane Mpas with Denominator. Part III: Non simple focal points and related bifurcations ”, International Journal of Bifurcation and Chaos, 15(2), 451-496, 2005.Downolad PDF 

A. Agliari, G.I. Bischi, R. Dieci, L. Gardini: “Global Bifurcations of Closed Invariant Curves: A computer assisted study”, International Journal of Bifurcation and Chaos, 15(4) pp. 1285-1328, 2005.Downolad PDF  

T. Puu, L. Gardini, I. Sushko: “A Hicksian Multiplier-Accelerator Model with Floor Determined by Capital Stock”, Journal of Economic Behavior and Organization, 56, pp. 331-348, 2005. Downolad PDF 

I. Sushko, L. Gardini, T. Puu: “Tongues of Periodicity in a Family of Two-dimensional Discontinuous Maps of Real Mobius Type ”, Chaos Solitons & Fractals, 21, pp. 403-412, 2004. Downolad PDF 

C. Chiarella, R. Dieci, L. Gardini, “The dynamic interaction of speculation and diversification ”, Applied Mathematical Finance, 12(1), pp. 17-52, 2005.Downolad PDF  

G.I. Bischi, R. Carini, L. Gardini e Paolo Tenti "Invito a : Sistemi dinamici e caos deterministico" Lettera Matematica Pristem (Springer-Italia) n. 47 (2003) pp. 15-26

Link (http://matematica.unibocconi.it/caos/home.htm) 

L. Gardini, I. Foroni, C. Mira: “A family of rational maps of the plane, with prefocal set at infinity”, Grazer Mathematische Berichte, 346 (Special Issue ECIT 2002), pp. 137-156, 2004.Downolad PDF  

A. Agliari, L. Gardini, C. Mira: “Transition from smooth to fractal boundaries in a class of two-dimensional endomorphisms”, Grazer Mathematische Berichte, 346 (Special Issue ECIT 2002), pp. 1-18, 2004.Downolad PDF  

C. Mira, G.I. Bischi, L. Gardini: “About a route to fractalization of basins generated by noninvertible plane maps”, Grazer Mathematische Berichte, 346 (Special Issue ECIT 2002), pp.299-312, 2004. Downolad PDF 

M. Gallegati, L. Gardini, T. Puu, I. Sushko: “Hicks Trade Cycle Revisited: Cycles and Bifurcations” Mathematics and Computers in Simulation, 63, pp. 505-527, 2003. Downolad PDF 

L. Gardini, I. Foroni, C. Mira: “On a particular foliation associated with a polynomial family of noninvertible maps of the plane”, International Journal of Bifurcation and Chaos, 14(5), pp. 1601-1624, 2004.Downolad PDF  

A. Agliari, C. Chiarella, L. Gardini “A Stability Analysis of the Perfect Foresight Map in nonlinear models of monetary dynamics”, Chaos Solitons & Fractals, 21(2), pp. 371-386, 2004. Downolad PDF 

R. Dieci, G.I. Bischi, L. Gardini "Routes to complexity in a business-cycle model described by a noninvertible triangular map”, Cubo A Mathematical Journal, Vol.5, N.3, pp.367-396, 2003. Downolad PDF 

Ilaria Foroni, Laura Gardini, J. Barkley Rosser Jr. “Adaptive and statistical expectations in a renewable resource market ”, Mathematics and Computers in Simulation, 63, pp. 541-567, 2003. Downolad PDF 

I.Sushko, T. Puu, L. Gardini : “The Hicksian floor-roof model for two regions linked by interregional trade ”, Chaos, Solitons & Fractals, 18, pp. 593-612, 2003.Downolad PDF  

A. Agliari, L. Gardini, C. Mira “On the fractal structure of basin boundaries in two-dimensional noninvertible maps”, International Journal of Bifurcation and Chaos, 13(7) (Special Issue ECIT 2000), pp. 1767-1785, 2003. Downolad PDF 

L. Gardini, G.I. Bischi, C. Mira “Invariant curves and focal points in a Lyness iterative process”, International Journal of Bifurcation and Chaos, 13(7) (Special Issue ECIT 2000), pp. 1841-1852, 2003. Downolad PDF 

G.I. Bischi, L. Gardini, C. Mira “Plane maps with denominator. Part II: noninvertible maps with simple focal points”, International Journal of Bifurcation and Chaos 13(8), pp 2253-2277, 2003.Downolad PDF  

I. Foroni, L. Gardini: “ Homoclinic bifurcations in Heterogeneous Market Models ”, Chaos, Solitons & Fractals, 15 (2003) 743-760.Downolad PDF 

A. Agliari, L. Gardini, T. Puu, “Global Bifurcations of basins in a Triopoly Game”, International Journal of Bifurcation and Chaos 12(10), 2002, pp. 2175-2207. Downolad PDF 

C. Chiarella, R. Dieci, L. Gardini, "Speculative behaviour and complex asset price dynamics: A global analysis" Journal of Economic Behavior and Organization, 49(1) 2002, pp. 173-197. Downolad PDF 

R. Dieci, G.I. Bischi and L. Gardini "Multistability and role of noninvertibility in a discrete-time business cycle model" Central European Journal of Operation Research , Vol. 9 (2001) pp. 71-96. Downolad PDF 

F. Bizzarri, M. Storace, L. Gardini, R. Lupini “Bifurcation analysis of a PWL chaotic circuit based on hysteresis through a one-dimensional map” International Journal of Bifurcation and Chaos, 11(7), pp. 1911-1927 (2001).Downolad PDF 

G.I. Bischi L. Gardini and C. Mira "Maps with a Vanishing Denominator. A Survey of some Results" Nonlinear Analysis, Theory, Methods and Applications, vol. 47/4 (Special Issue WCNA-2000), pp. 2171-2185 (2001).Downolad PDF 

G.I. Bischi and L. Gardini "Global Properties of Symmetric Competition Models with Riddling and Blowout Phenomena" Discrete Dynamics in Nature and Society vol. 5 (2000) pp. 149-160. Downolad PDF 

A. Agliari, L. Gardini, D. Delli Gatti, M. Gallegati "Global dynamics in a nonlinear model for the equity ratio”, Chaos, Soliton and Fractals, 11, pp.961-985 (2000). Downolad PDF 

R. Dieci, G.I. Bischi, L. Gardini "From Bi-stability to chaotic oscillations in a macroeconomic model”, Chaos Solitons & Fractals Vol 12 (No 5) (2001) pp. 805-822.Downolad PDF 

C. Chiarella, R. Dieci, L. Gardini, "Asset price dynamics in a financial market with fundamentalists and chartists " Discrete Dynamics in Nature and Society, Vol.6 (2001) pp.69-99. Downolad PDF 

A. Agliari, L. Gardini, T. Puu "The dynamics of a triopoly Cournot game” , Chaos, Solitons & Fractals, vol 11 (2000) pp. 2531-2560. Downolad PDF 

G.I. Bischi, C. Mira and L. Gardini «Unbounded sets of attraction», International Journal of Bifurcation and Chaos, vol. 10 n.6 pp. 1437-1469 (2000). Downolad PDF 

G.I. Bischi, C. Mammana and L. Gardini «Multistability and cyclic attractors in duopoly games», Chaos, Solitons and Fractals, 11, pp. 543-564 (2000). Downolad PDF 

G.I. Bischi, L. Gardini and M. Kopel «Analysis of Global Bifurcations in a Market Share Attraction Model», Journal of Economic Dynamics and Control ,  24, pp. 855-879 (2000), republished in “Complexity in Economics” The International Library of Critical Writings in Economics 174, edited by J. Barkley Rosser, Jr., Edward Elgar Publishing, UK (2004). Downolad PDF

G.I. Bischi, L. Gardini and C. Mira «Plane maps with denominator. Part 1: some generic properties», International Journal of Bifurcation and Chaos vol.9, n.1, (1999) pp 119-153. Downolad PDF 

L. Gardini, G.I. Bischi, D. Fournier-Prunaret «Basin boundaries and focal points in a map coming from Bairstow’s methods» CHAOS, vol.9 n.2 (1999). Downolad PDF 

E. Barucci, G.I. Bischi and L. Gardini «Endogenous fluctuations in a bounded rationality economy: learning non perfect foresight equilibria», Journal of Economic Theory, 87, 243-253 (1999).Downolad PDF  

G.I. Bischi, L. Gardini and C. Mira "Unbounded not diverging trajectories in maps with a vanishing denominator», in Annales Mathematicae Silesianae (special issue Proceedings ECIT98) vol. 13, pp. 91-102 (1999). 

G.I. Bischi, L. Gardini and C. Mira , "New phenomena related to the presence of focal points in two-dimensional maps», in Annales Mathematicae Silesianae (special issue Proceedings ECIT98) vol. 13, pp. 81-90 (1999). 

L. Gardini, G.I. Bischi and D. Fournier-Prunaret «Characterization of basin boundaries in Bairstow’s iterative methods» in Annales Mathematicae Silesianae (special issue Proceedings ECIT98) vol. 13, pp. 119-130 (1999). 

L. Gardini, G.I. Bischi "Foca1 points and focal values in rational maps", in Grazer Mathematische Berichte vol.339 (1999) (special issue Proceedings ECIT96, Gardini et al. editors), pp. 149-166.

L. Gardini, G.I. Bischi and R. Abraham "A bridge between Whitney's fold and cusp and the critical curves in two-dimensional endomorphisms" in Grazer Mathematische Berichte vol.339 (1999) (special issue Proceedings ECIT96, Gardini et al. editors), pp. 167-180. 

G.I. Bischi, L. Gardini "Foca1 points and basin fractalization in two classes of rational maps", in Grazer Mathematische Berichte vol.339 (1999) (special issue Proceedings ECIT96, Gardini et al. editors), pp. 61-84. 

I.M. Sushko, Y.L. Maistrenko, L. Gardini "On Chaotic attractors at the transition from homeomorphism to endomorphism in a family of two-dimensional piece-wise linear maps", in Grazer Mathematishe Berichte (special issue Proceedings ECIT96) Nr.339, pp.335-346, 1999. 

G.I. Bischi and L. Gardini «Role of invariant and minimal absorbing areas in chaos synchronization», Physical Review E, vol.58 n.5, (1998) pp. 5710-5719. Downolad PDF 

G.I. Bischi, L. Stefanini and L. Gardini «Synchronization, intermittency and critical curves in a duopoly game» Mathematics and Computers in Simulation, vol. 44, (1998) pp. 559-585.Downolad PDF 

G.I. Bischi and L. Gardini, «Basin fractalization due to focal points in a class of triangular maps», International Journal of Bifurcation and Chaos, vol.7 (7), (1997) pp. 1555-1577. 

Y.L. Maistrenko, I.M. Sushko, L. Gardini "About two mechanisms of reunion of chaotic attractors", Chaos, Soliton and Fractals, 9(8), (1998) pp. 1373-1390.Downolad PDF 

C.F. Frouzakis, L. Gardini, Y.G. Kevrekidis, G. Millerioux, C. Mira, "On some properties of invariant sets of two-dimensional noninvertible maps", International Journal of Bifurcation and Chaos 7(6), (1997) pp. 1167-1194. 

R. Lupini, S. Lenci, L. Gardini "Bifurcations and multistability in a class of two dimensional endomorphisms", Nonlinear Analysis T. M.& A 28(1), (1997) pp. 61-85. Downolad PDF 

R. Lupini, S. Lenci, L. Gardini "Poincaré maps of impulsed oscillators and chaotic dynamics", Il Nuovo Cimento B, 111B(4) (1996) pp. 427-454.

D. Fournier-Prunaret, C. Mira, L. Gardini "Some contact bifurcations in two-dimensional examples", in Grazer Mathematishe Berichte  (special issue Proceedings ECIT94), 1997. 

C. Mira, J.P. Carcasses, M. Gilles, L. Gardini "Plane foliation of two dimensional noninvertible maps", International Journal of Bifurcation and Chaos, 6(8), (1996) pp. 1439-1462. 

D. Delli Gatti, M. Gallegati, L. Gardini "Investment confidence, Corporate debt and lncome fluctuations", Journal of Economic Behavior and Organization, 22, (1993) pp. 161-187.Downolad PDF 

L. Gardini "Homoclinic bifurcations in n-dimensional endomorphisms, due to expanding periodic points'', Nonlinear Analysis, Theory, Methods & Applications, 23(8), (1994) pp. 1039-1089. 

L. Gardini, R. H. Abraham, D. Fournier Prunaret, R. J. Record "A double logistic map", International Journal of Bifurcation and Chaos, 4(1), (1994) pp. 145-176. 

C. Mira, D. Fournier-Prunaret, L. Gardini, H. Kawakami, J.C. Cathala "Basin bifurcations of two-dimensional noninvertible maps. Fractalization of basins", International Journal of Bifurcation and Chaos, 4(2) (1994) pp.343-381. 

L. Gardini, R. Lupini "One-dimensional chaos in impulsed linear oscillators", International Journal of Bifurcation and Chaos, 3(4) (1993) pp. 921-94l. 

L. Gardini "Some global bifurcations of two-dimensional endomorphisms by use of critical lines", Nonlinear Analysis, Theory, Methods & Applications, 18, (1992) pp. 361-399. 

Books and Edited Volumes

 

G.I. Bischi, R. Carini, L. Gardini e P. Tenti, Sulle Orme del Caos. Comportamenti complessi in modelli matematici semplici,  Bruno Mondadori Editore,  2004.

L. Gardini, G.L. Forti, D. Gronau, L. Paganoni (editors) "Proceeding of the European Conference on Iteration Theory 1996" , Special Issue of the Grazer Mathematishe Berichte, Nr.339, 1999.

R. Abraham, L. Gardini, C. Mira "Chaos in Discrete Dynamical Systems (A visual introduction in 2 dimensions)", TELOS, SPRINGER-VERLAG, N-Y 1997.

C. Mira, L. Gardini, A. Barugola, J.C. Cathala "Chaotic Dynamics in Two-Dimensional NonivertibIe Maps", WORLD-SCIENTIFIC Publ. Co., "Nonlinear Sciences, Series A", Singapore 1996.

R.L. D'Ecclesia, L. Gardini  Lezioni di Matematica Finanziaria, Parte I , Edizioni “Quattro Venti”, Libreria Goliardica, Urbino, 1997, Edizione Giappichelli (Torino), 1998(1° ediz.), 1999 (2° ediz.), 2000 (3° ediz.), 2001 (4° ediz.), 2004 (5° ediz.).

R.L. D'Ecclesia, L. Gardini Lezioni di Matematica Finanziaria, Parte II , Edizioni “Quattro Venti”, Libreria Goliardica, Urbino, 1997, Edizione Giappichelli (Torino), 1998 (1° ediz.), 2000 (2° ediz.).

 Contributions in Multiauthor Books and Proceedings

 

A.Agliari, G.I. Bischi and L.Gardini: "Chapter 1. Some Methods for the Global Analysis of Closed Invariant Curves in Two-Dimensional Maps", in "Business Cycle Dynamics - Models and Tools", T. Puu and I.Sushko Ed.s, Springer Verlag, 2006. Downolad PDF 

Iryna Sushko and Laura Gardini: "Chapter 2. Center Bifurcation for a Two-Dimensional Piecewise Linear Map", in "Business Cycle Dynamics - Models and Tools", T. Puu and I.Sushko Ed.s, Springer Verlag, 2006. Downolad PDF 

Laura Gardini, Tönu Puu and Iryna Sushko: "Chapter 6. The Hicksian Model with Investment Floorand Income Ceiling", in "Business Cycle Dynamics - Models and Tools", T. Puu and I.Sushko Ed.s, Springer Verlag, 2006. Downolad PDF 

Iryna Sushko, Tönu Puu and Laura Gardini: "Chapter 11. A Goodwin-type Model with a Piecewise Linear Investment Function", in "Business Cycle Dynamics - Models and Tools", T. Puu and I.Sushko Ed.s, Springer Verlag, 2006. Downolad PDF 

Laura Gardini, Tönu Puu and Iryna Sushko: "Chapter 12. A Goodwin-type Model with Cubic Investment Function", in "Business Cycle Dynamics - Models and Tools", T. Puu and I.Sushko Ed.s, Springer Verlag, 2006. Downolad PDF 

C. Chiarella, R. Dieci, L. Gardini, “Asset price dynamics and diversification with heterogeneous agents”, Proceedings WHEIA-2003, in T. Lux, S. Reitz and E. Samanidou Ed.s, (eds.), Nonlinear Dynamics and Heterogeneous Interacting Agents, Lecture Notes in Economics & Mathematical Systems, Springer, Vol. 550, 2005, pp. 251-267. Downolad PDF 

C. Chiarella, R. Dieci, L. Gardini, “A dynamic analysis of speculation across two markets”, in Gallegati, M., Kirman, A., Marsili, M. (eds.), The Complex Dynamics of Economic Interaction -  Essays in Economics and Econophysics, Lecture Notes in Economics & Mathematical Systems, Vol. 531, Springer, 2004, pp. 197-212. Downolad PDF 

I. Foroni and L. Gardini “Heterogeneous Models with Learning and Homoclinic Bifurcations ”, in “Heterogeneous Agents, Interactions and Economic Performance”, R. Cowan and N. Jonard (Eds.) Springer Verlag, 2003.

A.Agliari, G.I. Bischi and L. Gardini "Some methods for thr Global Analysis of Dynamic Games represented by Noninvertible Maps" Chapter 3 in Oligopoly Dynamics, Models and Tools, T. Puu and I. Sushko editors, Springer Verlag, 2002, pp. 31-83. Downolad PDF 

T. Puu, L. Gardini, I. Sushko: “Cournot duopoly with kinked demand according to Palander and Wald ”, Chapter 5 in Oligopoly Dynamics, Models and Tools, T. Puu and I. Sushko editors, Springer Verlag, 2002, pp. 111-146. Downolad PDF 

I.Sushko, L. Gardini, T. Puu: “Duopoly with piecewise linear discontinuous reaction functions”, Chapter 6 in Oligopoly Dynamics, Models and Tools, T. Puu and I. Sushko editors, Springer Verlag, 2002, pp. 147-169.Downolad PDF  

T. Puu, L. Gardini: “Hotelling type duopoly and oligopoly ”, Chapter 11 in Oligopoly Dynamics, Models and Tools, T. Puu and I. Sushko editors, Springer Verlag, 2002, pp. 265-310. Downolad PDF

M. Kopel, G.I. Bischi and L. Gardini «On new phenomena in dynamic promotional competition models with homogeneous and quasi-homogeneous firms», in Interaction and Market Structure. Essays on Heterogeneity in Economics. D. Delli Gatti, M. Gallegati and A.P. Kirman (Editors), Springer-Verlag, Lecture Notes in Economic and Mathematical Systems, vol. 484, pp. 57-87 (2000). 

L. Gardini, J. C. Cathala, C. Mira "Contact bifurcations of absorbing and chaotic areas in two-dimensional endomorphisms", in Iteration Theory, W. Forg-Rob et al ed.s, World Scientific, 1996, pp.100-111. 

L. Gardini, C. Mira, D. Fournier-Prunaret "Properties of invariant areas in two-dimensional endomorphisms", in Iteration Theory, W. Forg-Rob et al ed.s, World Scientific, 1996, pp. 112-125. 

L. Gardini "Homoclinic orbits of saddles in two-dimensional endomorphisms", in Iteration Theory, W. Forg-Rob et al Eds., World Scientific,1996, pp. 81-99. 

D. Delli Gatti, M. Gallegati, L. Gardini "Complex dynamics in a simple macroeconomic model with financing constraints", in New Perspectives in Monetary Macroeconomics, G.A. Dymski and R. Pollin Ed.s, Michigan University Press, 1993, pp. 51-76. 

L. Gardini "On a model of financial crisis. Critical Lines as new tools of glohal analysis", in Nonlinear Dynamics in Economics and Social Sciences, ed. F. Gori, L. Geronazzo e M. Galeotti, Springer-Verlag, N-Y,1993, pp. 252-263. 

L. Gardini "Global analysis and bifurcations in two-dimensional endomorphisms by use of critical curves", pp. 114-125 in European Conference on Iteration Theory 91",  J.P. Lampreira, J.Llibre, C. Mira, J. Sousa Ramos, G. Targonski (eds.), World Scientific, Singapore, 1992. 

   Submitted Papers, Research Reports and Working Papers

R. Dieci, I. Foroni, Laura Gardini, X-Z He “Market Mood, Adaptive Beliefs and Asset Price Dynamics”, Quantitative Finance Research Paper Series, n. 162, School of Finance and Economics, University of Technology Sydney, August 2005  (http://www.qfrc.uts.edu.au). 

C. Chiarella, Roberto Dieci and L. Gardini: “Asset price and wealth dynamics in a financial market with heterogeneous agents”, Quantitative Finance Research Paper Series, n. 134, School of Finance and Economics, University of Technology Sydney, October 2004 ,http://www.business.uts.edu.au/qfrc/research/publications.html). 

M. Ciaschini, R. Dieci and L. Gardini “Nonlinearity in a multi-sector dynamic model ”, Quaderni di Economia, Matematica e Statistica N.84, Università di Urbino (2003).

C. Chiarella, R. Dieci, L. Gardini, "A dynamic analysis of speculation across two markets", Quantitative Finance Research Paper Series, n. 89, School of Finance and Economics, University of Technology Sydney, January 2003 (http://www.business.uts.edu.au/qfrc/research/publications.html). 

A. Agliari, L. Gardini, C. Chiarella “Adaptive expectations in models of monetary dynamics” Contributi di ricerca in Econometria e Matematica. Istituto di Econometria e Matematica per le Decisioni Economiche, Università Cattolica del Sacro Cuore di Milano (2002).

I.Foroni, L. Gardini, J. Barkley Rosser Jr. “Adaptive and statistical expectations in a renewable resource market”, Università Cattolica del Sacro Cuore di Milano (2002). 

C. Chiarella, R. Dieci, L. Gardini, "Speculative Behaviour and Complex Asset Price Dynamics", Quantitative Finance Research Paper Series, n. 49, School of Finance and Economics, University of Technology Sydney, March 2001 (http://www.business.uts.edu.au/qfrc/research/publications.html)

G.I. Bischi and L. Gardini "Equilibrium selection and transient dynamics under adaptive and statistical learning" Quaderni dell’Istituto di Matematica "E. Levi", Università di Parma, n.9 (2000). Downolad PDF 

R. Dieci, L. Gardini and G.I. Bischi «Global dynamics in a Kaldor-type business cycle model», Quaderni dell’Istituto di Matematica «E. Levi», Università di Parma, n.4 (1998). 

G.I. Bischi and L. Gardini «Cycles and bifurcations in duopoly games», Quaderni dell’Istituto di Matematica «E. Levi», Università di  Parma, n.3 (1998). 

G.I. Bischi, L. Gardini «Trasformazioni puntuali iterate e caos deterministico», Quaderni dell’Istituto di Matematica «E. Levi», Università di Parma, n.1, (1998). 

G.I. Bischi, A. Naimzada, L. Gardini, «Infinite distributed memory in discrete dynamical systems». Quaderni di Economia, Matematica e Statistica, Facoltà di Economia, n. 39, Università di Urbino (1996).

G.I. Bischi, L. Gardini, «Mann Iterations Reducible to Plane Endomorphisms». Quaderni di Economia, Matematica e Statistica, Facoltà di Economia, n. 36, Università di Urbino (1996). 

---

Some Coauthors

Gian-Italo Bischi, University of Urbino (Italy)
Christian Mira,  Toulose (France)
Ralph Abraham, Visual Math Institute, Santa Cruz, California (USA)
Carl Chiarella, University of Technology, Sydney (Australia).
Michael Kopel, Vienna University of Technology (Austria)
Anna Agliari, Università Cattolica, Milan (Italy)
Mauro Gallegati, Università di Ancona (Italy)
Domenico Delli Gatti, Università Cattolica, Milan (Italy)
Daniele Fournier-Prunaret, INSA, Toulose (France)
J. Barkley Rosser,  Jr., James Madison University, Harrisonburg, USA
Tönu Puu, CERUM centre for Regional Sciences, Umea (Sweden)
Irina Sushko, National Academy of Sciences of Ukraine, Kiev (Ukraine)
Roberto Dieci, Università di Parma (Italy)
Ilaria Foroni, Università Cattolica, Milan (Italy)
Ahmad Naimzada, Università di Milano Bicocca, Milan (Italy)
Fabio Tramontana, Università Politecnica delle Marche, Ancona (Italy)
 

Useful links
 

Links to Universities of the world
Sulle Orme del Caos:  http://www.brunomondadori.com/sulleormedelcaos
Nonlinear Dynamics (frequently asked questions in nonlinear dynamics)
UK Nonlinear News
CeNDEF  (Center for Nonlinear Dynamics in Economics and Finance- University of Amsterdam
G.N.F.M. (Gruppo Nazionale per la Fisica Matematica)
A.M.A.S.E.S. (Associazione per la Matematica Applicata alle Scienze Economiche e Sociali)
CIMAB (Centro Interuniversitario per la Matematica Applicata a Biologia, Medicina ed Ambiente)
U.M.I. (Unione Matematica Italiana)
Centro interdipartimentale per lo Studio delle Dinamiche Complesse (CSDC)
Resource Modeling Association
Storia e Cultura Matematica Bocconi-Pristem
The MacTutor History of Mathematics Archive of St. Andrew University
SICC  (Società Italiana Caos e Complessità)
SCTPLS (Society for Chaos Theory in Psicology and Life Sciences)
CITG  (Centro Interuniversitario per la Teoria dei Giochi e le Applicazioni)
SIEC  (Social Interaction Economics & Computing)
Colloquium Mathematicum (Festival della Scienza, Genova)

Meetings, Workshops, Schools
Forthcoming.

Previous.
MDEF-2004 (Modelli Dinamici in Economia e Finanza) Urbino, September 16-18, 2004
International School: Topics in Nonlinear Dynamics Discrete Dynamical Systems and Applications,  Urbino, July 7-9, 2004
Summer School on Nonlinear Dynamical Systems in Economics, CISM, Udine,  June 7-11 2004XV-IMGTA (Italian Meeting on Game Theory and Applications)  Urbino, July 9-12, 2003
WEHIA 2003,  Kiel  29-31 May 2003
Eight Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, Vienna 14-16 May 2003

To print the PDF files you need an Acrobat Reader version >3: click here to download it Back to home page

Last modified: 28/04/2004 by G.I. B.