Examples of integrable sub-Riemannian geodesic flows
Dynamical Systems
2007-05-23 v2 Optimization and Control
Abstract
Motivated by a paper of Bolsinov and Taimanov DG/9911193 we consider non-holonomic situation and exhibit examples of sub-Riemannian metrics with integrable geodesic flows and positive topological entropy. Moreover the Riemannian examples are obtained as "holonomization" of sub-Riemannian ones. A feature of non-holonomic situation is non-compactness of the phase space. We also exhibit a Liouvulle-integrable Hamiltonian system with topological entropy of all integrals positive.
Cite
@article{arxiv.math/0105128,
title = {Examples of integrable sub-Riemannian geodesic flows},
author = {Boris Kruglikov},
journal= {arXiv preprint arXiv:math/0105128},
year = {2007}
}
Comments
21 pages; Answer to the self-posed question is added: Is it possible to construct Liouville-integrable Hamiltonian system with positive topological entropies of all integrals? Yes and we present an example