On special flows over IETs that are not isomorphic to their inverses

Przemysław Berk; Krzysztof Frączek

doi:10.3934/dcds.2015.35.829

Article Contents

2015, Volume 35, Issue 3: 829-855. Doi: 10.3934/dcds.2015.35.829

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On special flows over IETs that are not isomorphic to their inverses

Przemysław Berk^1, and
Krzysztof Frączek^1,

1.
Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100 Toruń

Received: March 2014

Revised: June 2014

Published: March 2015

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Abstract

In this paper we give a criterion for a special flow to be not isomorphic to its inverse which is a refine of a result in [6]. We apply this criterion to special flows $T^f$ built over ergodic interval exchange transformations $T:[0,1)\to[0,1)$ (IETs) and under piecewise absolutely continuous roof functions $f:[0,1)\to\mathbb{R}_+$. We show that for almost every IET $T$ if $f$ is absolutely continuous over exchanged intervals and has non-zero sum of jumps then the special flow $T^f$ is not isomorphic to its inverse. The same conclusion is valid for a typical piecewise constant roof function.

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Mathematics Subject Classification: Primary: 37A10, 37E35.

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