Normal Singular Geodesics of a Conformally Generic Sub-Riemannian Metric
Dynamical Systems
2025-12-23 v2 Differential Geometry
Abstract
We prove that a Ma\~n\'e generic real-analytic -Hamiltonian H, subjected to a totally non-holonomic real-analytic distribution , has no non-trivial normal -singular orbits of minimal rank. If has co-rank 1, this implies that , where is a generic real-analytic potential, does not admit non-trivial normal -singular orbits.
Cite
@article{arxiv.2505.17319,
title = {Normal Singular Geodesics of a Conformally Generic Sub-Riemannian Metric},
author = {Shahriar Aslani},
journal= {arXiv preprint arXiv:2505.17319},
year = {2025}
}