Limit cycles for piecewise smooth dynamical systems in dimension n>2 and in compact manifolds

• Grant number: 17/04689-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: June 01, 2017
• End date: February 28, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Ricardo Miranda Martins
• Grantee: Joyce Aparecida Casimiro
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 12/18780-0 - Geometry of Control Systems, Dynamical and Stochastics Systems, AP.TEM

Abstract

In this project we study the existence of limit cycles for two kind of dynamical systems: perturbations of piecewise smooth systems in R^n possessing a invariant compact submanifold filled by periodic orbits and also linear piecewise smooth dynamical systems on manifolds of the form M= R^n x ( S^k)^m. The case m=0, in particular when n2, has been exhaustively studied in the last years, so we consider n different from 0 and m,k\geq 1. We will show that the study of limit cycles for non-planar piecewise smooth vector fields is a very active research topic with very interesting results, motivating the student for more advanced studies in the area of piecewise smooth dynamical systems. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CASIMIRO, Joyce Aparecida. Limit cycles for piecewise smooth dynamical systems in dimension n>2 and in compact manifolds. 2019. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.