Rotation Set for Torus Homeomorphisms

• Grant number: 11/14122-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2011
• End date: January 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Fábio Armando Tal
• Grantee: Pablo Dávalos de La Peña
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this research project we study the relation between the rotation set and the dynamics of a homeomorphism of the two-torus. In the last decades this topic has had an intense development within the dynamical systems, showing that the rotation set is a rich source of information about the dynamics of a homeomorphism of $\T^2$ homotopic to the identity, analogously to the study of the rotation number for circle homeomorphisms, started by Henry Poincar\'e in the begining of the twentieth century. However, there are still unanswered basic questions: for instance, it is not well understood what kind of subsets of the plane can or cannot be realized as rotation sets of homeomorphisms of $\T^2$. In this project, we intend to construct new examples of rotation sets with non-empty interior realized by homeomorphisms. Also, we study new restrictions on the dynamics of a homeomorphism imposed by the rotation set, in the case it has non-empty interior.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DAVALOS, PABLO. ON ANNULAR MAPS OF THE TORUS AND SUBLINEAR DIFFUSION. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, v. 17, n. 4, p. 913-978, SEP 2018. (11/14122-5)