Finsler and sub-Finsler geodesics with chattering
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918039914545152 |
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| author | Lokutsievskiy, L. V. Zelikin, M. I. |
| author_facet | Lokutsievskiy, L. V. Zelikin, M. I. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_24474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finsler and sub-Finsler geodesics with chattering Lokutsievskiy, L. V. Zelikin, M. I. Differential Geometry Metric Geometry Optimization and Control 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. |
| title | Finsler and sub-Finsler geodesics with chattering |
| topic | Differential Geometry Metric Geometry Optimization and Control |
| url | https://arxiv.org/abs/2505.24474 |