On the nonexistence of isochronous tangential centers in Filippov vector fields
Abstract
The isochronicity problem is a classical problem in the qualitative theory of planar vector fields which consists in characterizing whether a center is isochronous or not, that is, if all the trajectories in a neighbourhood of the center have the same period. This problem is usually investigated by means of the socalled period function. In this paper, we are interested in exploring the isochronicity problem for tangential centers of planar Filippov vector fields. By computing the period function for planar Filippov vector fields around tangential centers, we show that such centers are never isochronous.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.09020
 Bibcode:
 2021arXiv211109020N
 Keywords:

 Mathematics  Dynamical Systems;
 34C23;
 34A36
 EPrint:
 To appear in Proceedings of the American Mathematical Society, 2022