27 Feb 2001

Boris Kruglikov "Positive topological entropy of integrable systems: Examples".

We exhibit non-holonomic geodesic flows on (contact) 3-dimensional manifolds with the properties: smooth integrability, polynomial non-integrability, positive topological entropy, zero measure entropy for smooth measures. The flows possess several features of the non-compact case but in essential part (on the critical set) they behave as the holonomic flows introduced by Bolsinov and Taimanov. This has an explanation by means of "holonomization" of the metric using the corresponding Reeb vector field. In addition this Reeb field has zero topological entropy. We finish with a discussion of a possible definition of the chaos.