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arXiv · 2505.24474

Finsler and sub-Finsler geodesics with chattering

L. V. Lokutsievskiy·M. I. Zelikin
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Abstract

In this paper, we provide examples of Finsler and sub-Finsler manifolds whose geodesics exhibit chattering, that is, a countable number of switches over an arbitrarily small time interval. We also present an explicit left-invariant structure on a Carnot group whose geodesics exhibit chattering. This provides a negative answer to Le Donne's question. Furthermore, the paper presents a sufficient condition for normal Pontryagin maximum principle extremals in (sub-)Finsler problems to exhibit chattering.

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BibTeXRIS

L. V. Lokutsievskiy, M. I. Zelikin. 2025-05-30. Finsler and sub-Finsler geodesics with chattering. https://arxiv.org/abs/2505.24474

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