Springer Proceedings in Mathematics #2: Dynamics, Games and Science II: Dyna 2008, in Honor of Maur CIO 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

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.

1 Network Control Analysis for Time-Dependent Dynamical States.- 2 Renormalization and Focal Decomposition.- 3 Micro-Foundation of the Social Change.- 4 Singularities, Walrasian Economics and Economic Crisis.- 5 Probabilistic Methods in Dynamical Analysis: Population Growths Associated to Models Beta (p,q) with Allee Effect.- 6 Power Indices Applied to Portuguese Parliament.- 7 A Methodological Contribution in the Theory of the Firm under Uncertainty.- 8 Explosion of Smoothness for Conjugacies Between Unimodal Maps.- 9 Multidimensional Rovella-Like Attractors.- 10 Robust Heteroclinic Behaviour, Synchronization, and Ratcheting of Coupled Oscillators.- 11 An Economical Model for Dumping.- 12 Fractional Control of Dynamic Systems.- 13 A Dynamical Point of View of Quantum Information: Discrete Wigner Measures.- 14 Dynamics on Spectral Solutions of Forced Burgers Equation.- 15 Area-Preserving Diffeomorphisms from the C1 Standpoint.- 16 A Theoretical, Multidisciplinary View of Catastrophic Regime Change.- 17 General Relativistic Elasticity - Statics and Dynamics of Spherically Symmetric Metrics.- 18 Post-Inflationary Scalar Field Phase Dynamics.- 19 An Application of the SIR Model to the Evolution of Epidemics in Portugal- 20 Poissonian Tree Constructed from Independent Poisson Point Processes.- 21 Hamiltonian Systems on Polyhedra.- 22 Patents Moving to Bankrupcy Boundaries.- 23 Computation of Genus and Braid Index for Renormalizable Lorenz Links.- 24 Statistical Stability for Equilibrium States.- 25 Dynamic Games of Network Effects.- 26 Exit Times and Persistence of Solitons for a Stochastic Korteweg-de-Vries Equation.- 27 Optimization Approach to a Simulation Algorithm of a Mixer-Settler System in the Transient State.- 28 Duality Theory, Representation Formulas and Uniqueness Results for Viscosity Solutions of Hamilton-Jacobi Equations.- 29 Microscopic Dynamics for the Porous Medium Equation.- 30 A Model for Wolf's Sunspot Numbers.- 31 On Topological Classification of Morse-Smale Diffeomorphisms.- 32 Isentropic Dynamics and Control in an Economic Model for Capital Accumulation.- 33 Hydrodynamic Limit of the Exclusion Process in Inhomogeneous Media.- 34 Application of Fractional Order Concepts in the Study of Electrical Potential.- 35 Economics of Bioenergy Crops for Electricity Generation: Implications for Land Use and Greenhouse Gases.- 36 An H-Theorem for Chemically reacting Gases.- 37 Dynamics, Systems, Dynamical Systems and Interaction Graphs.- 38 The Dynamics of Scalar Fields in Cosmology.- 39 Resort Prices and Bankruptcy.- 40 On the Hannay-Ozorio de Almeida Sum Formula.- 41 A Fourier Transform Method for Relaxation of Kinetic Equations.- 42 Bethe Ansatz Solution of the Finite Bernoulli Matching Model of Sequence Alignment.- 43 Fitness Function Evaluation Through Fractional Algorithms.- 44 An Exponential Observer for Systems on SE(3) with Implicit Outputs.- 45 Stability of Polydeuces Orbit.- 46 Peixoto Classification of 2-Dim Flows Revisited.- 47 Fractional Control of Legged Robots.- 48 Evolutionary Dynamics of the Spatial Prisoner's Dilemma with Single and Multi-Behaviors - a Multi-Agent Application.- 49 Euclidean Jordan Algebras and Strongly Regular Graphs.- 50 Parameter Estimation in Stochastic Differential Equations.- 51 Stochastic Saddle Paths and Economic Theory.