English

A Piecewise Smooth $\lambda$-Lemma

Dynamical Systems 2025-07-16 v1

Abstract

In this paper we provide extensions of the λ\lambda-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}
}