Invariant manifolds for piecewise smooth differential systems in $\mathbb{R}^{3}$
Dynamical Systems
2020-12-29 v1
Abstract
In this paper some piecewise smooth perturbations of a three-dimensional differential system are considered. The existence of invariant manifolds filled by periodic orbits is obtained after suitable small perturbations of the original differential system. These manifolds emerge from a continuum of cylinders of which does exist for the piecewise smooth differential systems after a rotation of some planar algebraic polynomial curves. The main tool used in order to obtain the results is the averaging theory for piecewise smooth differential systems.
Cite
@article{arxiv.2012.13951,
title = {Invariant manifolds for piecewise smooth differential systems in $\mathbb{R}^{3}$},
author = {Claudio A. Buzzi and Rodrigo D. Euzébio and Ana C. Mereu},
journal= {arXiv preprint arXiv:2012.13951},
year = {2020}
}