Creation of Limit Cycles in Piecewise Smooth Vector Fields Tangent to Nested Tori

Author(s)

Carvalho, Tiago ; Goncalves, Luiz Fernando

• Document type: Journal article
• Source: Qualitative Theory of Dynamical Systems; v. 20, n. 2, p. 21-pg., 2021-07-01.

Abstract

The main goal of this paper is to present the behavior generated by piecewise smooth vector fields tangent to foliations. We consider two smooth foliations F1 and F2 that are coupled to produce a foliation composed by nested topological tori. Moreover, a piecewise smooth vector field composed of periodic orbits and tangent to these tori is considered. We perturb this piecewise vector field (and, consequently, the foliations) and the birth of either finite or infinitely many limit cycles for the 3D piecewise smooth vector field is observed. (AU)

• FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
• Grantee: Claudio Aguinaldo Buzzi
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 19/10450-0 - Piecewise smooth vector fields: Closing Lemmas, shifts and horseshoe dynamics.
• Grantee: Tiago de Carvalho
• Support Opportunities: Regular Research Grants