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Extreme relations for topological flows

Kamiński B., Siemaszko A., Szymański J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 1

17--24

We introduce the concept of an extreme relation for a topological flow as an analogue of the extreme measurable partition for a measure-preserving transformation considered by Rokhlin and Sinai, and we show that every topological flow has such a relation for any invariant measure. From this result, it follows, among other things, that any deterministic flow has zero topological entropy and any flow which is a K-system with respect to an invariant measure with full support is a topological K-flow.