No Periodic normal Geodesics in $J^k(\mathbb{R},\mathbb{R}^n)$
Dynamical Systems
2022-05-16 v2 Differential Geometry
Abstract
The space of -jets of real function of one real variable admits the structure of a Carnot group, which then has an associated Hamiltonian geodesic flow. As in any Hamiltonian flow, a natural question is the existence of periodic solutions. Does the space of -jets have periodic geodesics? This study will demonstrate the integrability of subRiemannian geodesic flow, characterize and classify the subRiemannian geodesics in the space of -jets, and show that they are never periodic.
Keywords
Cite
@article{arxiv.2205.06156,
title = {No Periodic normal Geodesics in $J^k(\mathbb{R},\mathbb{R}^n)$},
author = {Alejandro Bravo-Doddoli},
journal= {arXiv preprint arXiv:2205.06156},
year = {2022}
}