Global dynamics of piecewise smooth dynamical systems

• Grant number: 18/03338-6
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2018
• End date: April 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ricardo Miranda Martins
• Grantee: Ricardo Miranda Martins
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The main aim of this project is to study global phenomena in piecewise smooth dynamical systems, continuing some recent works developed by the proponent. Among the main topics to be studied are (i) the existence of limit cycles in piecewise smooth dynamical systems defined on compact manifolds, (ii) the existence of Poincaré-Hopf-like theorems for pseudo-equilibria and (iii) the appearance of chaotic behavior in piecewise smooth systems, including Shilnikov-like phenomena. (AU)

Scientific publications

(5)

(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, APR 25 2021. (18/03338-6, 18/16430-8, 19/10269-3, 19/06873-2, 18/13481-0, 17/23692-6)

DA SILVA, GUILHERME TAVARES; MARTINS, RICARDO MIRANDA. Dynamics and stability of non-smooth dynamical systems with two switches. NONLINEAR DYNAMICS, v. 108, n. 4, p. 28-pg., 2022-04-13. (18/03338-6, 21/08031-9, 18/13481-0)

ANDRADE, K. DA S.; JEFFREY, M. R.; MARTINS, R. M.; TEIXEIRA, M. A.. On the Dulac's problem for piecewise analytic vector fields. Journal of Differential Equations, v. 266, n. 4, p. 2259-2273, FEB 5 2019. (13/07523-9, 18/03338-6, 12/18780-0, 15/06903-8, 14/21259-5)

ANDRADE, KAMILA DA S.; JEFFREY, MIKE R.; MARTINS, RICARDO M.; TEIXEIRA, MARCO A.. Homoclinic Boundary-Saddle Bifurcations in Planar Nonsmooth Vector Fields. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 32, n. 04, p. 27-pg., 2022-03-30. (18/13481-0, 21/08031-9, 15/06903-8, 12/18780-0, 18/03338-6, 14/21259-5, 13/07523-9)

GRAMA, LINO; MARTINS, RICARDO M.; PATRAO, MAURO; SECO, LUCAS; SPERANCA, LLOHANN. The projected homogeneous Ricci flow and its collapses with an application to flag manifolds. MONATSHEFTE FUR MATHEMATIK, v. 199, n. 3, p. 28-pg., 2022-09-10. (18/03338-6, 21/08031-9, 18/13481-0)