Closed poly-trajectories and Poincaré index of non-smooth vector fields on the plane
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Data
2013-04-01
Autores
Buzzi, C. A. [UNESP]
De Carvalho, T. [UNESP]
Da Silva, P. R. [UNESP]
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Resumo
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 Poincaré Index for non-smooth vector fields is introduced. © 2013 Springer Science+Business Media New York.
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closed poly-trajectory, heteroclinic orbits, Limit cycles, non-smooth vector fields, Poincaré index, singular perturbation, vector fields, Heteroclinic orbit, Limit cycle, Non-smooth vector fields, Poincare, Singular perturbations, Vector fields, Trajectories, Vectors
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Journal of Dynamical and Control Systems, v. 19, n. 2, p. 173-193, 2013.