Empirical measures in Dynamics

• Grant number: 23/03954-7
• Support Opportunities: Scholarships in Brazil - Master
• Start date: June 01, 2023
• End date: March 31, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Ali Tahzibi
• Grantee: Lucas Viana Reis
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 17/06463-3 - Probabilistic and algebraic aspects of smooth dynamical systems, AP.TEM

Abstract

In this project, we will study empirical measures of smooth dynamical systems. Essentially, we explore two phenomena. First, we analyze systems that have physical measures with intermingled basins. Next, we will prove the existence of dynamical systems with non-statistical (historical) behavior on the boundary of systems that have measures with intermingled basins.