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Thom-Smale Program for piecewise smooth differential systems in low dimensions manifolds

Grant number: 17/08779-8
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): September 01, 2017
Effective date (End): January 26, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Claudio Aguinaldo Buzzi
Grantee:Ana Livia Rodero
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
Associated scholarship(s):19/00440-7 - Study of limit cycles in piecewise smooth systems on the sphere, BE.EP.DR

Abstract

The project is dedicated to the study of piecewise smooth vector fields, defined in two or three dimensional manifolds. Within this context, a study will first be carried out aiming at a classification of structurally stable systems in two-dimensional compact manifolds. In a second phase we will consider the bifurcation set, which is obtained by excluding the structurally stable systems, and we will make a classification of the systems of codimension one. Finally the project will be concluded with a characterization of structurally stable systems defined in 3-dimensional manifolds that are foliated by compact 2-dimensional manifolds.