Closed poly-trajectories and Poincaré index of non-smooth vector fields on the plane - Buzzi, C. A. [UNESP]; De Carvalho, T. [UNESP]; Da Silva, P. R. [UNESP] (My University, 2013)
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.
Keywords: 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