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
• Start date: August 01, 2023
• End date: 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
• Institution abroad: 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)