Planar reversible vector fields, averaging theory and polycycles in non-smooth vector fields

Author(s)

Paulo Henrique Reis Santana

• Document type: Master's Dissertation
• Press: São José do Rio Preto. 2021-07-15.
• Institution: Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto
• Defense date: 2021-06-28
• Advisor: Claudio Aguinaldo Buzzi; Jaume Llibre

Abstract

In this work one will see the phase portraits, in the Poincaré disk, of the local normal forms of symmetrical singularities of reversible vector fields of type (2; 0) and (2; 1); an application of the Averaging Theory at the field of Astrophysics, aiming the study of the periodic orbits in a model of the Friedmann-Robertson-Walker universe; and some generalizations of well established results about the polycycles in smooth vector fields to the non-smooth cases, aiming a better understanding of its stability and the bifurcation of limit cycles. (AU)

• FAPESP's process: 18/23194-9 - Global study of reversible vector fields of type (2,0)
• Grantee: Paulo Henrique Reis Santana
• Support Opportunities: Scholarships in Brazil - Master