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

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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 Poincaré Index for non-smooth vector fields is introduced.

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Authors and Affiliations

  1. UNESP - Univ Estadual Paulista, So Jos do Rio Preto, So Paulo, Brazil

    C. A. Buzzi & P. R. da Silva

  2. UNESP - Univ Estadual Paulista, Bauru, So Paulo, Brazil

    T. de Carvalho

Authors
  1. C. A. Buzzi
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  2. T. de Carvalho
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  3. P. R. da Silva
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Correspondence to C. A. Buzzi.

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Buzzi, C.A., de Carvalho, T. & da Silva, P.R. Closed poly-trajectories and Poincaré index of non-smooth vector fields on the plane. J Dyn Control Syst 19, 173–193 (2013). https://doi.org/10.1007/s10883-013-9169-4

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  • DOI: https://doi.org/10.1007/s10883-013-9169-4

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