Measures of maximal entropy beyond uniform hyperbolicity

• Grant number: 24/22609-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: July 01, 2025
• End date: June 30, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Yuri Gomes Lima
• Grantee: Juan Carlos Mongez Duran
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The aim of the project is to determine conditions that guarantee a system with weak forms of hyperbolicity (partially hyperbolic or non-uniformly hyperbolic) to have finitely many measures of maximal entropy. We state 8 projects, in a variety of contexts that include diffeomorphisms and flows, and propose approaches that use many tools, including Markov partitions, homoclinic classes and the specification property.