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Closing lemmas and shifts for piecewise smooth vector fields

Grant number: 17/18255-6
Support type:Scholarships in Brazil - Doctorate (Direct)
Effective date (Start): January 01, 2018
Effective date (End): February 28, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Tiago de Carvalho
Grantee:Andre do Amaral Antunes
Home 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 to which the orbit returns infinitely many times in its neighborhood. 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 lemma, 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. The student will focus on obtaining results related to versions of Closing lemma (where it is possible and where it is impossible to establish?) for piecewise smooth vector fields. Moreover, in the study of such recurrences we will establish conjugations between shifts (of finite and infinite symbols) and first return maps, in this way, we will obtain ergodic results regarding piecewise smooth vector fields. (AU)

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Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
ANTUNES, Andre do Amaral. . 2021. Doctoral Thesis - Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto São José do Rio Preto.

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