A Piecewise Smooth $\lambda$-Lemma
Dynamical Systems
2025-07-16 v1
Abstract
In this paper we provide extensions of the -Lemma (also known as Inclination Lemma) for piecewise smooth vector fields and maps. In order to achieve our main result, we investigate the regularity of time-T-maps of piecewise smooth vector fields defined at crossing orbits. We prove that these maps are homeomorphisms and also piecewise smooth diffeomorphisms.
Keywords
Cite
@article{arxiv.2507.10896,
title = {A Piecewise Smooth $\lambda$-Lemma},
author = {Claudio A. Buzzi and Paulo Santana and Luan V. M. F. Silva},
journal= {arXiv preprint arXiv:2507.10896},
year = {2025}
}