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Ergodicity criterion for partially hyperbolic flows and flexibility of Lyapunov exponents for geodesic flows

Grant number: 23/05100-5
Support Opportunities:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): August 01, 2023
Effective date (End): June 30, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Gabriel Ponce
Grantee:Ygor Arthur Cesar de Jesus
Supervisor: Federico Juan Rodríguez Hertz
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Research place: Pennsylvania State University, United States  
Associated to the scholarship:21/02913-0 - Ergodic properties and flexibility of Lyapunov exponents for partially hyperbolic flows, BP.DR

Abstract

The aim of this project is to extend the understanding of some classes of partially hyperbolic systems such as partially hyperbolic geodesic flows regarding their ergodic and asymptotic properties. So far, we have developed a criterion for ergodicity of partially hyperbolic flows, which has lead naturally to the study of a theory of Blenders for flows. Also, as part of the program of creating tools to understand those classes of systems, we intend to develop a theory of perturbation and flexibility of Lyapunov Exponents inside some classes of systems, such as geodesic flows and symplectic diffeomorphisms. (AU)

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