Examples of integrable sub-Riemannian geodesic flows

Details Examples of integrable sub-Riemannian geodesic flows Examples of integrable sub-Riemannian geodesic flows

2001-05-16

arxiv.org/abs/math/0105128v2

Mathematics

Dynamical Systems

21 pages; Answer to the self-posed question is added: Is it possible to construct Liouville-integrable Hamiltonian system with

Scientific paper

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.

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