Invariant measures in weakly hyperbolic dynamics

• Grant number: 18/06267-2
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: July 02, 2018
• End date: August 10, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Edson Vargas
• Grantee: Edson Vargas
• Visiting researcher: Sun Wenxiang
• Visiting researcher institution: Peking University (PKU), China
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 16/25053-8 - Dynamics and geometry in low dimensions, AP.TEM

Abstract

The main goal of this project is to prove that invariant measures for weakly hyperbolic diffeomorphisms and flows with singularities can be approximated on the weak topology by periodic measures supported on hyperbolic periodic orbits. This result extends results we proved before and have applications in the context of dispersing billiards. This project is a continuation of some recent published works resulted from a collaboration of the visitor and the host and having a partial support from Fapesp. (AU)