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Structural stability of piecewise smooth dynamical systems on torus and spheres

Grant number: 17/23692-6
Support Opportunities:Scholarships in Brazil - Master
Effective date (Start): March 01, 2018
Effective date (End): February 29, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Ricardo Miranda Martins
Grantee:Matheus Manzatto de Castro
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
Associated scholarship(s):19/06873-2 - Piecewise smooth and reversible dynamical systems in R^(2n+1): existence of homoclinic trajectories and applications, BE.EP.MS

Abstract

In this project we will study the main theorem on structural stability for piecewise smooth dynamical systems on low dimensions. In particular, we will consider the global dynamics of families of piecewise smooth dynamical systems on torus $\mathbb R^2$, where the quantity of fold points have serious implications about the structural stability of the system. Moreover, on spheres $S^k$, $k=2,3$, we will obtain some results about the structural stability of piecewise smooth dynamical systems that are tangent to the Reeb foliation of $S^3$. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
CASTRO, MATHEUS M.; MARTINS, RICARDO M.; NOVAES, DOUGLAS D.. Anote on Vishik's normal form. Journal of Differential Equations, v. 281, p. 442-458, . (18/03338-6, 18/16430-8, 19/10269-3, 19/06873-2, 18/13481-0, 17/23692-6)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
CASTRO, Matheus Manzatto de. Local and 'sigma'-semilocal structural stability structural of piecewise smooth vector fields in compact 3-dimensional manifolds. 2020. Master's Dissertation - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.

Please report errors in scientific publications list by writing to: gei-bv@fapesp.br.