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arXiv · 2607.09618

Homoclinic Theorems for piecewise smooth vector fields

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

In this paper we provide extensions of the Birkhoff-Smale Homoclinic Theorem and the $\lambda$-Lemma for piecewise smooth vector fields free of sliding motion. We prove that if the vector field is $T$-periodic in its independent variable and has a transverse homoclinic point, then its time-$T$-map is conjugated with a Bernoulli Shift and thus the vector field is chaotic. The Bernoulli Shifts considered here may have any finite number of symbols, or countably infinite many.

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Claudio Buzzi, Paulo Santana, Luan V. M. F. Silva. 2026-07-10. Homoclinic Theorems for piecewise smooth vector fields. https://arxiv.org/abs/2607.09618

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