Stable manifolds for periodically perturbed maps
Dynamical Systems
2023-11-08 v1
Abstract
We prove that if a certain entry in the map of the Hadamard-Perron theorem is -periodic in one of the variables, then the stable manifold guaranteed by the Hadamard-Perron theorem is a graph of a -periodic function. As an application, we extend the classical Levinson's result about the occurrence of an attracting closed invariant curve near a stable cycle of a system of autonomous equations under periodic perturbations to hybrid differential equations.
Cite
@article{arxiv.2311.03728,
title = {Stable manifolds for periodically perturbed maps},
author = {Matthew Williams and Oleg Makarenkov},
journal= {arXiv preprint arXiv:2311.03728},
year = {2023}
}