English

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 TT-periodic in one of the variables, then the stable manifold guaranteed by the Hadamard-Perron theorem is a graph of a TT-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.

Keywords

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}
}
R2 v1 2026-06-28T13:13:37.269Z