On deterministic and Kolmogorov extensions for topological flows

Abstract

The concepts of deterministic and Kolmogorov extensions of topological flows are introduced. We show that the class of deterministic extensions contains distal extensions and moreover that for the deterministic extensions the relative topological entropy vanishes and hence they preserve the topological entropy. On the other hand we relate the Kolmogorov extensions to the asymptotic ones and we show that the class of these extensions contains uniquely ergodic u.p.e. extensions and also the class of flows admitting an invariant relative $K$-measure with full support.

The main tool used to get these results is the relative version of the Rokhlin-Sinai theorem concerning the existence of perfect measurable partitions.