Rotation set for torus homeomorphisms

• Grant number: 13/01232-2
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: August 01, 2013
• End date: February 28, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Fábio Armando Tal
• Grantee: Guilherme Silva Salomão
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this research project we intend to study the relationship between the rotation set and dynamics of a torus homeomorphism. In recent decades this topic has been a very active field of research in dynamical systems, showing that the rotation set is a rich source of information about the dynamics of a torus homeomorphism which is homotopic to the identity as well as the study of the rotation number for homeomorphisms of the circle, introduced by mathematician Henry Poincaré in the last century. However, there are still very basic questions: for example, it is not entirely clear what type of plane subsets may or may not be made as rotation sets of torus homeomorphisms. In this project we propose the construction of new examples of rotation sets with nonempty interior realized by some torus homeomorphism. Moreover we studied new restrictions on the dynamics of a homeomorphism given by the rotation set in the case where it has empty interior. (AU)

Academic Publications

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

SALOMÃO, Guilherme Silva. Inexistence of sublinear diffusion for a class of torus homeomorphisms. 2019. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.