Transitive and entropy for homeomorphisms of surface

• Grant number: 14/12872-5
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: November 01, 2014
• End date: February 28, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Fábio Armando Tal
• Grantee: Everton Juliano da Silva
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 11/16265-8 - Low dimensional dynamics, AP.TEM

Abstract

In this research project we intend to study the relationship between entropy and transitivity for homeomorphisms of compact orientable surfaces which are homotopic to the identity. The study of such homeomorphisms through strictly topological methods is an area that has been active for the last 25 years, but the development of significant techniques and the refinement in the last decade has enable the solution of several fundamental problems that remained open. In this research project we intend to use the newly developed equivariant Brouwer theory to extend the results of Franks e Handel on area preserving homeomorphisms of the sphere with zero topological entropy. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SILVA, Everton Juliano da. Entropy estimates and a stronger theorem on the existence of horseshoes for a forcing theory for surface homeomorphism. 2019. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.