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arXiv · 1002.4169

Canard Cycles and Poincaré Index of Non-Smooth Vector Fields on the Plane

Claudio Buzzi·Tiago de Carvalho·Paulo Ricardo da Silva
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Abstract

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for the existence of canard kind solutions. By means of a regularization we prove that the canard cycles are singular orbits of singular perturbation problems which are limit periodic sets of a sequence of limit cycles. Moreover, we generalize the Poincaré Index for non-smooth vector fields.

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Claudio Buzzi, Tiago de Carvalho, Paulo Ricardo da Silva. 2010-05-17. Canard Cycles and Poincaré Index of Non-Smooth Vector Fields on the Plane. https://doi.org/10.1007/s10883-013-9169-4

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