Bumpy metric theorem for co-rank 1 sub-Riemannian and reversible sub-Finsler metrics

TL;DR

This paper proves that for a generic class of co-rank 1 sub-Riemannian and reversible sub-Finsler metrics, all strictly normal periodic orbits are non-degenerate, contributing to the understanding of their dynamical stability.

Contribution

It establishes a bumpy metric theorem for co-rank 1 sub-Riemannian and reversible sub-Finsler metrics, showing generic non-degeneracy of periodic orbits.

Findings

All strictly normal periodic orbits are non-degenerate for generic metrics.

The result applies to fixed co-rank 1 distributions.

It extends the understanding of periodic orbit stability in sub-Riemannian geometry.

Abstract

We prove that for a generic sub-Riemannian and reversible sub-Finsler metrics defined on a fixed co-rank 1 distribution, all strictly normal periodic orbits are non-degenerate.