Dynamics Games and Science I : DYNA 2008 in Honor of Maurício Peixoto and David Rand University of Minho Braga Portugal September 8 12 2008 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. 1 A Brief Survey of Focal Decompositon 2 Anosov and Circle Diffeomorphisms 3 Evolutionarily Stable Strategies and Replicator Dynamics in Asymmetric Two Population Games 4 Poverty Traps Rationality and Evolution 5 Leadership Model 6 Lorenz Like Chaotic Attractors Revised 7 A Dynamical Point of View of Quantum Information: Entropy and Pressure 8 Generic Hamiltonian Dynamical Systems: An Overview 9 Microeconomic Model Based on MAS Framework: Modeling an Adaptive Producer 10 Equilibrium in a Tourism Model with Different Types 11 Computability and Dynamical Systems 12 Dynamics and Biological Thresholds 13 Global Convergence in Difference Equations 14 Networks Synchronizability Local Dynamics and Some Graph Invariants 15 Continuous Models for Generic Evolution in Large Population 16 Forecasting of Yield Curves using Local State Space Reconstruction 17 KAM Theory as a Limit of Renormalization 18 An Overview of Optimal Life Insurance Purchase Consumption and Investment Problems 19 Towards a Theory of Periodic Difference Equations and it Applications to Population Dynamics 20 Thompsons Group Teichmüller Spaces and Dual Riemann Surfaces 21 A Modified Model of an Edgeworthian Economy 22 Fractional Analysis of Traffic Dynamics 23 The Set of Planar Orbits of Second Species in the RTBP 24 Statistical Properties of the Maximum for Non Uniformly Hyperbolic Dynamics 25 Adaptive Learning and Central Bank Inattentiveness in Optimal Monetary Policy 26 Discrete Time Finite State Space Mean Field Games 27 Sample Exclusion Process: from Randomness to Determination 28 Universality in PS120 Fluctuations 29 Dynamical Systems with Nontrivially Recurrent Invariant Manifolds 30 Some Recent Results on the Stability of Endomorphisms 31 Differential Rigidity and Applications in One Dimensional Dynamics 32 Minimum Regret Pricing of Contingent Claims in Incomplete Markets 33 A Class of Infinite Dimensional Replicator Dynamics 34 Kinetic Theory for Chemical Reactions Without a Barrier 35 Dynamical Gene Environmental Networks Under Ellipsoidal Uncertainty Set Theoretic Regression Analysis Based on Ellipsoidal OR 36 Strategic Interaction in Macroeconomic Policies: An Outline of a New Differential Game Approach. 37 Renormalization of Hénon Maps 38 Application of Fractional Calculus in Engineering 39 Existence of Invariant Circles for Infinitely Renormalisable Area Preserving Maps 40 The Dynamics of Expectations 41 Dynamics on the Circle 42 Rolling Ball Problems 43 On the Dynamics of Certain Models Describing the HIV Infection 44 Tilings and Bussola for Making Decisions. 45 A Hotelling Type Network 46 The Closing Lemma in Retrospect 47 From Peixotos Theorem to Palis Conjecture 48 Dynamics Associated to Games (Fictitious Play) with Chaotic Behavior 49 A Finite Time Blowup Result for Quadratic ODEs 50 Relating Material and Space Time Metrics Within Relativistic Elasticity: a Dynamical Example 51 Strategic Information Revelation Through Real Options in Investment Games 52 On Consumption Indivsibilites the Demand for Durables and Income Distribution.