About the Editors: Mauricio Peixoto, in1953, together with Leopoldo Nachbin, helped to found IMPA (Instituto Nacional de Matematica 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. Aragao de Carvalho, Diogo Pinheiro, Alberto A. Pinto and Mauricio 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

• 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 Thompson's 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 ReplicatorDynamics.- 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 Peixoto's 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.