Structural Stability of Piecewise Smooth Dynamical Systems on Torus and Spheres

• Grant number: 17/23692-6
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2018
• End date: 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 $S^3$.

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

CASTRO, MATHEUS M.; MARTINS, RICARDO M.; NOVAES, DOUGLAS D.. Anote on Vishik's normal form. Journal of Differential Equations, v. 281, p. 442-458, APR 25 2021. (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.