Examples of integrable sub-Riemannian geodesic flows

2001/05/16 by Boris Kruglikov, Kruglikov, Boris
Mathematics · #37B40 #37J30 #37J60 #53C17 #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #math.DS #math.OC #msc:37B40 #msc:37J30 #msc:37J60 #msc:53C17

paper · pdf · doi:10.48550/arxiv.math/0105128

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

arxiv created 2001/10/22 · arxiv updated 2009/11/30

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.

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