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Study of limit cycles in piecewise smooth systems on the sphere

Grant number: 19/00440-7
Support type:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): September 01, 2019
Effective date (End): July 26, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Claudio Aguinaldo Buzzi
Grantee:Ana Livia Rodero
Supervisor abroad: Joan Torregrosa I Arus
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
Local de pesquisa : Universitat Autònoma de Barcelona (UAB), Spain  
Associated to the scholarship:17/08779-8 - Thom-Smale Program for piecewise smooth differential systems in low dimensions manifolds, BP.DR


At first, this study aims to classify centers for a special class of piecewise smooth Ordinary Differential Equations defined in the unit sphere. In a second moment, we would like to obtain an upper bound for the number of limit cycles that bifurcate from the center. If this upper bound there exists, we will try to answer the question: how does it depend on the degree of the polynomial perturbations and of the order of perturbation?