English

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 DD-Hamiltonian H, subjected to a totally non-holonomic real-analytic distribution DD, has no non-trivial normal DD-singular orbits of minimal rank. If DD has co-rank 1, this implies that H+uH + u, where uu is a generic real-analytic potential, does not admit non-trivial normal DD-singular orbits.

Keywords

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}
}