Dynamics with critical points of mixed criticality

• Grant number: 11/01482-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Effective date (Start): June 01, 2011
• Effective date (End): January 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Edson Vargas
• Grantee: Simon Trevor Lloyd
• 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

The aim of this research is to consider the existence of wandering intervals for the class ofcircle homeomorphisms with critical points withmixed criticality. By this we mean that thecriticality as we approach the critical pointfrom above is not equal to the criticality as weapproach from below. Such maps occur naturally inthe study of flows on surfaces with saddle connections.Once the topological picture is clear, we will consider properties of the invariant measures,the fine geometric structure, and the question ofmetric rigidity. We shall also seek to generalizeany results from circle homeomorphisms to other one-dimensional settings, such as smooth maps ofthe circle with a flat interval, and look at the applications to the topological theory of vectorfields on surfaces. (AU)

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)

LLOYD, SIMON; VARGAS, EDSON. CRITICAL COVERING MAPS WITHOUT ABSOLUTELY CONTINUOUS INVARIANT PROBABILITY MEASURE. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v. 39, n. 5, p. 2393-2412, MAY 2019. (17/10106-1, 11/01482-3)