Sub-Riemannian structures on groups of diffeomorphisms
Optimization and Control
2015-08-19 v2
Abstract
In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We derive the Hamiltonian geodesic equations for such structures, and we provide examples of normal and of abnormal geodesics in that infinite-dimensional context. The momentum formulation gives a sub-Riemannian version of the Euler-Arnol'd equation. Finally, we establish some approximate and exact reachability properties for diffeomorphisms, and we give some consequences for Moser theorems.
Cite
@article{arxiv.1409.8378,
title = {Sub-Riemannian structures on groups of diffeomorphisms},
author = {Sylvain Arguillere and Emmanuel Trélat},
journal= {arXiv preprint arXiv:1409.8378},
year = {2015}
}