Finsler and sub-Finsler geodesics with chattering
Differential Geometry
2025-06-02 v1 Metric Geometry
Optimization and Control
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.
Keywords
Cite
@article{arxiv.2505.24474,
title = {Finsler and sub-Finsler geodesics with chattering},
author = {L. V. Lokutsievskiy and M. I. Zelikin},
journal= {arXiv preprint arXiv:2505.24474},
year = {2025}
}