Dynamics, Games and Science I: DYNA 2008, in Honor of Maurício Peixoto and David Rand, University of Minho, Braga, Portugal, September 8-12, 2008 (Springer Proceedings in Mathematics Book 1)

Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further. V. 1. 1. A Brief Survey Of Focal Decomposition / Mauricio M. Peixoto -- 2. Anosov And Circle Diffeomorphisms / João P. Almeida, Albert M. Fisher, Alberto A. Pinto, And David A. Rand -- 3. Evolutionarily Stable Strategies And Replicator Dynamics In Asymmetric Two-population Games / Elvio Accinelli And Edgar J. Sánchez Carrera -- 4. Poverty Traps, Rationality And Evolution / Elvio Accinelli, Silvia London, Lionello F. Punzo, And Edgar J. Sanchez Carrera -- 5. Leadership Model / Leandro Almeida, José Cruz, Helena Ferreira, And Alberto A. Pinto -- 6. Lorenz-like Chaotic Attractors Revised / Vítor Araújo And Maria José Pacifico -- 7. A Dynamical Point Of View Of Quantum Information: Entropy And Pressure / A.t. Baraviera, C.f. Lardizabal, A.o. Lopes, And M. Terra Cunha -- 8. Generic Hamiltonian Dynamical Systems: An Overview / Má́rio Bessa And João Lopes Dias --^ 9. Microeconomic Model Based On Mas Framework: Modeling An Adaptive Producer / Pavel Brazdil And Frederico Teixeira --10. A Tourist's Choice Model / Brida, M.j. Defesa, M. Faias, And Alberto A. Pinto --11. Computability And Dynamical Systems / J. Buescu, D.s. Graça, And N. Zhong -- 12. Dynamics And Biological Thresholds / N.j. Burroughs, M. Ferreira, J. Martins, B.m.p.m. Oliveira, Alberto A. Pinto, And N. Stollenwerk -- 13. Global Convergence In Difference Equations / Elias Camouzis And Gerasimos Ladas --14. Networks Synchronizability, Local Dynamics And Some Graph Invariants / Acilina Caneco, Sara Fernandes, Clara Grácio, And J. Leonel Rocha -- 15. Continuous Models For Genetic Evolution In Large Populations / Fabio A.c.c. Chalub And Max O. Souza -- 16. Forecasting Of Yield Curves Using Local State Space Reconstruction / Eurico O. Covas And Filipe C. Mena -- 17. Kam Theory As A Limit Of Renormalization / João Lopes Dias --^ 18. An Overview Of Optimal Life Insurance Purchase, Consumption And Investment Problems / Isabel Duarte, Diogo Pinheiro, Alberto A. Pinto, And Stanley R. Pliska -- 19. Towards A Theory Of Periodic Difference Equations And Its Application To Population Dynamics / Saber N. Elaydi, Rafael Luı́s, And Henrique Oliveira -- 20. Thompson's Group, Teichmüller Spaces, And Dual Riemann Surfaces / Edson De Faria -- 21. Bargaining Skills In An Edgeworthian Economy / M. Ferreira, B. Finkenstädt, B.m.p.m. Oliveira, Alberto A. Pinto, And A.n. Yannacopoulos --22. Fractional Analysis Of Traffic Dynamics /lino Figueiredo And J.a. Tenreiro Machado -- 23. The Set Of Planar Orbits Of Second Species In The Rtbp / Joaquim Font, Ana Nunes, And Carles Simó -- 24. Statistical Properties Of The Maximum For Non-uniformly Hyperbolic Dynamics /ana Cristina Moreira Freitas, Jorge Milhazes Freitas, And Mike Todd --^ 25. Adaptive Learning And Central Bank Inattentiveness In Optimal Monetary Policy / Orlando Gomes, Vivaldo M. Mendes, And Diana A. Mendes -- 26. Discrete Time, Finite State Space Mean Field Games / Diogo A. Gomes, Joana Mohr, And Rafael Rigão Souza -- 27. Simple Exclusion Process: From Randomness To Determinism / Patrícia Gonnçalves -- 28. Universality In Psi20 Fluctuations / Rui Gonçalves, Helena Ferreira, And Alberto A. Pinto -- 29. Dynamical Systems With Nontrivially Recurrent Invariant Manifolds / Viacheslav Grines And Evgeny Zhuzhoma -- 30. Some Recent Results On The Stability Of Endomorphisms / J. Iglesias, A. Portela, And A. Rovella -- 31. Differential Rigidity And Applications In One-dimensional Dynamics / Yunping Jiang -- 32. Minimum Regret Pricing Of Contingent Claims In Incomplete Markets /c. Kountzakis, S.z. Xanthopoulos, And A.n. Yannacopoulos --^ 33. A Class Of Infinite Dimensional Replicator Dynamics./ D. Kravvaritis, V. Papanicolaou, T. Xepapadeas, And A.n. Yannacopoulos -- 34. Kinetic Theory For Chemical Reactionswithout A Barrier / Gilberto M. Kremer And Ana Jacinta Soares -- 35. Dynamical Gene-environment Networks Under Ellipsoidal Uncertainty: Set-theoretic Regression Analysis Based On Ellipsoidal Or /erik Kropat, Gerhard-wilhelmweber, And Selma Belen -- 36. Strategic Interaction In Macroeconomic Policies: An Outline Of A New Differential Game Approach / T. Krishna Kumar --37. Renormalization Of Hénon Maps / M. Lyubich And M. Martens -- 38. Application Of Fractional Calculus In Engineering/ J.a. Tenreiro Machado, Isabel S. Jesus, Ramiro Barbosa, Manuel Silva, And Cecilia Reis -- 39. Existence Of Invariant Circles For Infinitely Renormalisable Area-preservingmaps / R.s. Mackay -- 40. The Dynamics Of Expectations /wilfredo L. Maldonado And Isabel M.f. Marques -- 41. Dynamics On The Circle /w. De Melo --^ 42. Rolling Ball Problems / Waldyr M. Oliva And Gláucio Terra -- 43. On The Dynamics Of Certain Models Describing The Hiv Infection / Dayse H. Pastore And Jorge P. Zubelli -- 44. Tilings And Bussola For Making Decisions / Alberto A. Pinto, Abdelrahim S. Mousa, Mohammad S. Mousa, And Rasha M. Samarah -- 45. A Hotelling-type Network / Alberto A. Pinto And Telmo Parreira -- 46. The Closing Lemma In Retrospect./ Charles Pugh -- 47. From Peixoto's Theorem To Palis's Conjecture / Enrique R. Pujals -- 48. Dynamics Associated To Games (fictitious Play) With Chaotic Behavior / Colin Sparrow And Sebastian Van Strien -- 49. A Finite Time Blowup Result For Quadratic Ode's / Dennis Sullivan -- 50. Relating Material And Space-time Metrics Within Relativistic Elasticity: A Dynamical Example / E.g.l.r. Vaz, Irene Brito, And J. Carot -- 51. Strategic Information Revelation Through Real Options In Investment Games / Takahiro Watanabe --^ 52. On Consumption Indivisibilities, The Demand For Durables, And Income Distribution./ David Zilberman And Jenny Hsing-i. Mauricio Matos Peixoto, Alberto Adrego Pinto, David A. Rand, Editors. Includes Bibliographical References. Front Matter....Pages i-xxxi A Brief Survey of Focal Decomposition....Pages 1-10 Anosov and Circle Diffeomorphisms....Pages 11-23 Evolutionarily Stable Strategies and Replicator Dynamics in Asymmetric Two-Population Games....Pages 25-35 Poverty Traps, Rationality and Evolution....Pages 37-52 Leadership Model....Pages 53-59 Lorenz-Like Chaotic Attractors Revised....Pages 61-79 A Dynamical Point of View of Quantum Information: Entropy and Pressure....Pages 81-121 Generic Hamiltonian Dynamical Systems: An Overview....Pages 123-137 Microeconomic Model Based on MAS Framework: Modeling an Adaptive Producer....Pages 139-157 A Tourist’s Choice Model....Pages 159-167 Computability and Dynamical Systems....Pages 169-181 Dynamics and Biological Thresholds....Pages 183-191 Global Convergence in Difference Equations....Pages 193-219 Networks Synchronizability, Local Dynamics and Some Graph Invariants....Pages 221-238 Continuous Models for Genetic Evolution in Large Populations....Pages 239-242 Forecasting of Yield Curves Using Local State Space Reconstruction....Pages 243-251 KAM Theory as a Limit of Renormalization....Pages 253-270 An Overview of Optimal Life Insurance Purchase, Consumption and Investment Problems....Pages 271-286 Towards a Theory of Periodic Difference Equations and Its Application to Population Dynamics....Pages 287-321 Thompson’s Group, Teichmüller Spaces, and Dual Riemann Surfaces....Pages 323-338 Bargaining Skills in an Edgeworthian Economy....Pages 339-352 Fractional Analysis of Traffic Dynamics....Pages 353-357 The Set of Planar Orbits of Second Species in the RTBP....Pages 359-363 Statistical Properties of the Maximum for Non-Uniformly Hyperbolic Dynamics....Pages 365-374 Adaptive Learning and Central Bank Inattentiveness in Optimal Monetary Policy....Pages 375-383 Discrete Time, Finite State Space Mean Field Games....Pages 385-389 Simple Exclusion Process: From Randomness to Determinism....Pages 391-403 Universality in PSI20 fluctuations....Pages 405-420 Dynamical Systems with Nontrivially Recurrent Invariant Manifolds....Pages 421-470 Some Recent Results on the Stability of Endomorphisms....Pages 471-485 Differential Rigidity and Applications in One-Dimensional Dynamics....Pages 487-502 Minimum Regret Pricing of Contingent Claims in Incomplete Markets....Pages 503-528 A Class of Infinite Dimensional Replicator Dynamics....Pages 529-532 Kinetic Theory for Chemical Reactions Without a Barrier....Pages 533-543 Dynamical Gene-Environment Networks Under Ellipsoidal Uncertainty: Set-Theoretic Regression Analysis Based on Ellipsoidal OR....Pages 545-571 Strategic Interaction in Macroeconomic Policies: An Outline of a New Differential Game Approach....Pages 573-595 Renormalization of Hénon Maps....Pages 597-618 Application of Fractional Calculus in Engineering....Pages 619-629 Existence of Invariant Circles for Infinitely Renormalisable Area-Preserving Maps....Pages 631-636 The Dynamics of Expectations....Pages 637-649 Dynamics on the Circle....Pages 651-659 Rolling Ball Problems....Pages 661-669 On the Dynamics of Certain Models Describing the HIV Infection....Pages 671-688 Tilings and Bussola for Making Decisions....Pages 689-708 A Hotelling-Type Network....Pages 709-720 The Closing Lemma in Retrospect....Pages 721-741 From Peixoto’s Theorem to Palis’s Conjecture....Pages 743-746 Dynamics Associated to Games (Fictitious Play) with Chaotic Behavior....Pages 747-759 A Finite Time Blowup Result for Quadratic ODE’s....Pages 761-762 Relating Material and Space-Time Metrics Within Relativistic Elasticity: A Dynamical Example....Pages 763-767 Strategic Information Revelation Through Real Options in Investment Games....Pages 769-784 On Consumption Indivisibilities, the Demand for Durables, and Income Distribution....Pages 785-809 "Dynamics, Games and Science I and II" are a selection of surveys and research articles written by leading researchers in mathematics and its applications to the sciences. The majority of the contributions are on dynamical systems and game theory, focusing either on some of their most fundamental and theoretical developments or on their applications to modeling in biology, economics, engineering, finances and psychology. The aim of these books is to present cutting-edge research in these areas that can encourage graduate students and researchers in mathematics to develop them further A selection of surveys and research articles written by researchers in mathematics and its applications to the sciences. It focuses on dynamical systems and game theory, and on some of their most fundamental and theoretical developments or on their applications to modeling in biology, economics, engineering, finances and psychology.