## Dynamics, Games and Science I: DYNA 2008, in Honor of Maurício Peixoto and David Rand, University of Minho, Braga, Portugal, September 8-12, 2008Mauricio Matos Peixoto, Alberto Adrego Pinto, David A. J. Rand 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

1 | |

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 |