Extreme Relations for Topological Flows

Volume 53 / 2005

Brunon Kamiński, Artur Siemaszko, Jerzy Szymański Bulletin Polish Acad. Sci. Math. 53 (2005), 17-24 MSC: Primary 37B05; Secondary 37B40, 37A35. DOI: 10.4064/ba53-1-3

Abstract

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.

Authors

  • Brunon KamińskiFaculty of Mathematics
    and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail
  • Artur SiemaszkoFaculty of Mathematics
    and Computer Science
    University of Warmia and Mazury
    Żołnierska 14A
    10-561 Olsztyn, Poland
    e-mail
  • Jerzy SzymańskiFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toruń, Poland
    e-mail

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