Piecewise smooth vector fields on compact manifolds

• Grant number: 21/08031-9
• Support Opportunities: Regular Research Grants
• Duration: November 01, 2021 - October 31, 2023
• 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

In this project, we will continue to study piecewise smooth dynamical systems that are defined in compact manifolds. While the local theory of piecewise smooth dynamical systems is in a fairly advanced stage, the same cannot be said about its global properties. The main aim of this project is to study (i) the existence of periodic orbits and other invariant sets and (ii) the establishment of Poincaré-Hopf type results for such systems. (AU)

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)

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, 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)