Geodesic
Extreme Relations for Topological Flows
Brunon Kamiński 1   ; Artur Siemaszko 2   ; Jerzy Szymański 1
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
2 Faculty of Mathematics and Computer Science University of Warmia and Mazury Żołnierska 14A 10-561 Olsztyn, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 1, pp. 17-24 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba53-1-3
Keywords: introduce concept extreme relation topological flow analogue extreme measurable partition measure preserving transformation considered rokhlin sinai every topological flow has relation invariant measure result follows among other things deterministic flow has zero topological entropy flow which k system respect invariant measure full support topological k flow

Brunon Kamiński  1   ; Artur Siemaszko  2   ; Jerzy Szymański  1

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
2 Faculty of Mathematics and Computer Science University of Warmia and Mazury Żołnierska 14A 10-561 Olsztyn, Poland 
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Brunon Kamiński; Artur Siemaszko; Jerzy Szymański. Extreme Relations for Topological Flows. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 1, pp. 17-24. doi: 10.4064/ba53-1-3

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