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Induced flows

Published:1973 Issue:0 Volume:177 Page:375-390
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Petersen Karl,Shapiro Leonard

Abstract

The construction of induced transformations is considered in the setting of topological dynamics. Sufficient conditions are given for induced flows to be topologically weakly mixing, and it is proved that Toeplitz flows and certain Sturmian flows satisfy these conditions and give rise to new and easily constructed classes of flows which have entropy zero and are uniquely ergodic, minimal, and topologically weakly mixing. An example is given of a weakly mixing minimal flow which is not topologically strongly mixing.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1973-177-00/S0002-9947-1973-0322839-1/S0002-9947-1973-0322839-1.pdf

Reference26 articles.

1. The entropy of a derived automorphism;Abramov, L. M.;Dokl. Akad. Nauk SSSR,1959

2. Topological entropy;Adler, R. L.;Trans. Amer. Math. Soc.,1965

3. Point transitive flows, algebras of functions and the Bebutov system;Auslander, Jozeph;Fund. Math.,1967

4. Annals of Mathematics Studies, No. 44;Furstenberg, Harry,1960

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