Normal Singular Geodesics of a Conformally Generic Sub-Riemannian Metric
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917161598976000 |
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| author | Aslani, Shahriar |
| author_facet | Aslani, Shahriar |
| contents | We prove that a Mañé generic real-analytic $D$-Hamiltonian H, subjected to a totally non-holonomic real-analytic distribution $D$, has no non-trivial normal $D$-singular orbits of minimal rank. If $D$ has co-rank 1, this implies that $H + u$, where $u$ is a generic real-analytic potential, does not admit non-trivial normal $D$-singular orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17319 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Normal Singular Geodesics of a Conformally Generic Sub-Riemannian Metric Aslani, Shahriar Dynamical Systems Differential Geometry 53C17, 37J06 We prove that a Mañé generic real-analytic $D$-Hamiltonian H, subjected to a totally non-holonomic real-analytic distribution $D$, has no non-trivial normal $D$-singular orbits of minimal rank. If $D$ has co-rank 1, this implies that $H + u$, where $u$ is a generic real-analytic potential, does not admit non-trivial normal $D$-singular orbits. |
| title | Normal Singular Geodesics of a Conformally Generic Sub-Riemannian Metric |
| topic | Dynamical Systems Differential Geometry 53C17, 37J06 |
| url | https://arxiv.org/abs/2505.17319 |