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arXiv · 2507.10896

A Piecewise Smooth $\lambda$-Lemma

Claudio A. Buzzi·Paulo Santana·Luan V. M. F. Silva
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Abstract

In this paper we provide extensions of the $\lambda$-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.

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Claudio A. Buzzi, Paulo Santana, Luan V. M. F. Silva. 2025-07-15. A Piecewise Smooth $\lambda$-Lemma. https://arxiv.org/abs/2507.10896

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