Some distinct formulations of closing Lemmas

• Grant number: 17/05260-1
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2017
• End date: December 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Tiago de Carvalho
• Grantee: Andre do Amaral Antunes
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 13/24541-0 - Ergodic and qualitative theory of dynamical systems, AP.TEM

Abstract

In a given dynamic system it is possible to have points in the domain to which the orbit returns infinitely many times to it neighborhood. The Closing Lemma seeks to establish when perturbations of the initial system have a periodic orbit and thus the orbit "closes", hence the name of the lemma.Throughout this project we will study several formulations of Closing Lemmas, where the type of domain or the differentiability of the functions used are varied. For some of these formulations it is known that the response to the existence of the closed orbit is positive, for other formulations it is known that the answer is negative and there are still other formulations where there is no definitive answer. (AU)