Minimal sets in non-smooth dynamical systems

• Grant number: 15/06903-8
• Support Opportunities: Regular Research Grants
• Duration: July 01, 2015 - June 30, 2017
• 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 study the existence of minimal invariant sets in non-smooth dynamical systems. In particular, we are interested in the existence of limit cycles and homoclinic cycles in dimensions $2$ and $3$.In dimension $2$ we focus on the existence of homoclinic cycles for non-smooth systems with two zones, considering the cases saddle-focus and saddle-center (real and virtual). We also want to study the existence of limit cycles for non-smooth dynamical systems with a circle as discontinuity manifold.In dimension $3$ we study the existence of limit cycles and homoclinic orbits in the special case of a model presenting two parallel $T$-singularities. (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)

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)

LLIBRE, JAUME; MARTINS, RICARDO MIRANDA; TONON, DURVAL JOSE. Limit Cycles of Piecewise Smooth Differential Equations on Two Dimensional Torus. Journal of Dynamics and Differential Equations, v. 30, n. 3, p. 1011-1027, SEP 2018. (15/06903-8)

MARTINS, RICARDO M.; TONON, DURVAL J.. The chaotic behaviour of piecewise smooth differential equations on two-dimensional torus and sphere. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, v. 34, n. 2, p. 356-373, APR 3 2019. (15/06903-8)

LAMB, JEROEN S. W.; LIMA, MAURICIO F. S.; MARTINS, RICARDO M.; TEIXEIRA, MARCO ANTONIO; YANG, JIAZHONG. On the Hamiltonian structure of normal forms at elliptic equilibria of reversible vector fields in R-4. Journal of Differential Equations, v. 269, n. 12, p. 30-pg., 2020-12-05. (09/18338-2, 15/06903-8)

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)