Canard Cycles and Poincar\'e Index of Non-Smooth Vector Fields on the Plane
Dynamical Systems
2015-03-13 v2
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 Poincar\'e Index for non-smooth vector fields.
Cite
@article{arxiv.1002.4169,
title = {Canard Cycles and Poincar\'e Index of Non-Smooth Vector Fields on the Plane},
author = {Claudio Buzzi and Tiago de Carvalho and Paulo Ricardo da Silva},
journal= {arXiv preprint arXiv:1002.4169},
year = {2015}
}
Comments
20 pages, 25 figures