Dynamics, Games and Science I: DYNA 2008, in Honor of Maurício Peixoto and David Rand, University of Minho, Braga, Portugal, September 8-12, 2008

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Mauricio Matos Peixoto, Alberto Adrego Pinto, David A. J. Rand
Springer Science & Business Media, Mar 29, 2011 - Mathematics - 809 pages
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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.

 

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Contents

A Brief Survey of Focal Decomposition
1
Anosov and Circle Diffeomorphisms
11
Evolutionarily Stable Strategies and Replicator Dynamics in Asymmetric TwoPopulation Games
24
Poverty Traps Rationality and Evolution
37
Leadership Model
53
LorenzLike Chaotic Attractors Revised
60
A Dynamical Point of View of Quantum Information Entropy and Pressure
81
Generic Hamiltonian Dynamical Systems An Overview
122
Universality in PSI20 fluctuations
405
Dynamical Systems with Nontrivially Recurrent Invariant Manifolds
421
Some Recent Results on the Stability of Endomorphisms
471
Differential Rigidity and Applications in OneDimensional Dynamics
486
Minimum Regret Pricing of Contingent Claims in Incomplete Markets
503
A Class of Infinite Dimensional Replicator Dynamics
529
Kinetic Theory for Chemical Reactions Without a Barrier
533
Dynamical GeneEnvironment Networks Under Ellipsoidal Uncertainty SetTheoretic Regression Analysis Based on Ellipsoidal OR
545

Microeconomic Model Based on MAS Framework Modeling an Adaptive Producer
139
A Tourists Choice Model
158
Computability and Dynamical Systems
169
Dynamics and Biological Thresholds
182
Global Convergence in Difference Equations
193
Networks Synchronizability Local Dynamicsand Some Graph Invariants
220
Continuous Models for Genetic Evolution in Large Populations
239
Forecasting of Yield Curves Using Local State Space Reconstruction
243
KAM Theory as a Limit of Renormalization
253
An Overview of Optimal Life Insurance Purchase Consumption and Investment Problems
271
Towards a Theory of Periodic Difference Equations and Its Application to Population Dynamics
287
Thompsons Group Teichmuller Spaces and Dual Riemann Surfaces
322
Bargaining Skills in an Edgeworthian Economy
339
Fractional Analysis of Traffic Dynamics
353
The Set of Planar Orbits of Second Species in the RTBP
359
Statistical Properties of the Maximum for NonUniformly Hyperbolic Dynamics
364
Adaptive Learning and Central Bank Inattentiveness in Optimal Monetary Policy
375
Discrete Time Finite State Space Mean Field Games
385
Simple Exclusion Process From Randomness to Determinism
390
Strategic Interaction in Macroeconomic Policies An Outline of a New Differential Game Approach
572
Renormalization of Hénon Maps
597
Application of Fractional Calculus in Engineering
619
Existence of Invariant Circles for Infinitely Renormalisable AreaPreserving Maps
630
The Dynamics of Expectations
637
Dynamics on the Circle
651
Rolling Ball Problems
660
On the Dynamics of Certain Models Describing the HIV Infection
671
Tilings and Bussola for Making Decisions
689
A HotellingType Network
709
The Closing Lemma in Retrospect
721
From Peixotos Theorem to Paliss Conjecture
742
Dynamics Associated to Games Fictitious Play with Chaotic Behavior
747
A Finite Time Blowup Result for Quadratic ODEs
761
Relating Material and SpaceTime Metrics Within Relativistic Elasticity A Dynamical Example
763
Strategic Information Revelation Through Real Options in Investment Games
768
On Consumption Indivisibilities the Demand for Durables and Income Distribution
785
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About the author (2011)

About the Editors:

Maurício Peixoto, in1953, together with Leopoldo Nachbin, helped to found IMPA (Instituto Nacional de Matemática Pura e Aplicada), to which has been associated ever since and is a Emeritus Researcher at the present; Peixoto’s Theorem.is a key stone in mathematics and its extensions form a central area of research in dynamical systems.

Peixoto introduced the concept of focal decomposition in dynamical systems. Awards and Honors 1969 Moinho Santista Prize for Mathematics and in 1987 received the Third World Academy of Science Award in Mathematics; 1975-1977 President of the Brazilian Mathematical Society; 1979-1980 President of the National Research Council; 1981-1991 President of the Brazilian Academy of Sciences;

David Rand is Professor of Mathematics and is the co-director of the Systems Biology Centre, at University of Warwick. David Rand has made lasting contributions to pure and applied dynamical systems, and also to game theory, economics, theoretical physics, fluid dynamics, ecology and epidemiology, immunology and circadian rhythms. Rand published a dynamical game based on Cournot duopoly and showed that under rather natural conditions this game would have chaotic trajectories. His most recent work is on the interface between mathematics and systems biology. Awards and Honors 1986 Whitehead Prize of the London Mathematical Society. 1988 Wolfson Research Award. 1988 Founding editor of Nonlinearity 2004 Fellow, Institute of Mathematics and Its Applications (by invitation) 2005 Britten Lecturer. McMaster University 2006 EPSRC Senior Research Fellowship Alberto A. Pinto is Professor of Mathematics at University of Porto and, previously, was Professor of Mathematics at University of Minho. Edson de Faria, Welington de Melo and Alberto A. Pinto have developed a theory in the global hyperbolicity of renormalization for smooth unimodal mappings that is published in Annals of Mathematics Alberto A. Pinto, David Rand and Dennis Sullivan have developed an extensive theory characterizing the flexibility and rigidity of one and two dimensional hyperbolic dynamical systems and constructed Teichmuller spaces for them, in particular, for their conjugacy classes. This work has appeared in a number of papers and has been collected into a monograph that was published by Springer in 2008. Aragão de Carvalho, Diogo Pinheiro, Alberto A. Pinto and Maurício Peixoto are working in the semiclassical quantization of the pendulum equation using renormalization methods. Awards and Honors 1984- Augusto Martins prize at University of Porto 2007-Espinho town’s golden medal

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