Closed poly-trajectories and Poincar, index of non-smooth vector fields on the plane

Author(s)

Buzzi, C. A. ^[1] ; de Carvalho, T. ^[2] ; da Silva, P. R. ^[1]

Affiliation

^[1] UNESP Univ Estadual Paulista, So Jos Do Rio Preto, So Paulo - Brazil

^[2] UNESP Univ Estadual Paulista, Bauru, So Paulo - Brazil

• Document type: Journal article
• Source: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS; v. 19, n. 2, p. 173-193, APR 2013.
• Web of Science Citations: 6

Abstract

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a class of non-smooth vector fields we provide necessary and sufficient conditions for the existence of closed poly-trajectorie. By means of a regularization process we prove that hyperbolic closed poly-trajectories are limit sets of a sequence of limit cycles of smooth vector fields. In our approach the Poincar, Index for non-smooth vector fields is introduced. (AU)

• FAPESP's process: 10/18190-2 - Singularities of 3D piecewise smooth Filippov systems
• Grantee: Tiago de Carvalho
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 12/00481-6 - Regularization, singular perturbation and Averaging method applied to piecewise smooth vector fields
• Grantee: Tiago de Carvalho
• Support Opportunities: Regular Research Grants
• FAPESP's process: 07/08707-5 - Study of minimal sets for discontinuous systems via singular perturbations
• Grantee: Tiago de Carvalho
• Support Opportunities: Scholarships in Brazil - Doctorate