Continuity of entropy and classification of partially hyperbolic systems with one-dimensional central bundle

• Grant number: 17/13160-7
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: September 12, 2017
• End date: September 23, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Edson Vargas
• Grantee: Edson Vargas
• Visiting researcher: Radu Saghin
• Visiting researcher institution: Pontificia Universidad Católica de Valparaíso (PUCV), Chile
• 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

This project has two parts: 1. The study of the continuity of the topological entropy and of the metric entropy for partially hyperbolic systems with low dimensional center and the regularity of Lyapunov exponents associated to invariant bundles. 2. Classification of partially hyperbolic systems with one-dimensional center and eventual density of periodic orbits in the nonwandering set. (AU)