  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.
