Ergodic and qualitative theory of dynamical systems

Abstract

Dynamical systems are one of the best tools for understanding of the mathematical models of experimental sciences. The main goal of this project is to improve the knowledge of these systems obtaining new results with emphasis on the study of the following ten main topics: systems of differential equations piecewise smooth, discontinuous perturbations of centers, systems of quadratic polynomial differential equations in three dimensional space, reversible vector fields, stochastic adding machine and Julia sets, holomorphic dynamics and complex Hénon maps, periodic points for piecewise smooth maps and interval exchange, entropy of symplectic diffeomorphisms, accessibility for partially hyperbolic diffeomorphisms, and selection of measures the Gibbs-absolute zero temperature equilibrium. The main institution is the UNESP - S. J. Rio Preto. The team consists of researchers with experience in advising doctorates and coordinating projects, as well as young researchers. The team has also members from other campuses of UNESP: Bauru, Ilha Solteira, Presidente Prudente, and other institutions of the state of São Paulo: IME-USP, IMECC-UNICAMP and USP-Ribeirão Preto. The project will be guided by the following actions: i) cooperation with high level researches from Brazil and other countries as France, Spain, England, USA, Austria, Chile and Uruguay; ii) participation in conferences and visits to centers of excellence; iii) publication of results in journals of recognized scientific merit. (AU)