Exponential return times in a zero-entropy process

Paulina Grzegorek; Michal Kupsa

doi:10.3934/cpaa.2012.11.1339

Article Contents

2012, Volume 11, Issue 3: 1339-1361. Doi: 10.3934/cpaa.2012.11.1339

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Exponential return times in a zero-entropy process

Paulina Grzegorek^1, and
Michal Kupsa^2,

1.
Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wybrzeże Wysńskiego 27, 50-370 Wrocław
2.
Institute of Information Theory and Automation, The Academy of Sciences of the Czech Republic, Prague 8, CZ-18208

Received: November 30, 2010

Revised: March 31, 2011

Published: April 2012

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Abstract

We construct a zero-entropy weakly mixing finite-valued process with the exponential limit law for return resp. hitting times. This limit law is obtained in almost every point, taking the limit along the full sequence of cylinders around the point. Till now, the exponential limit law for return resp. hitting times, taking the limit along the full sequence of cylinders, have been obtained only in positive-entropy processes satisfying some strong mixing conditions of Rosenblatt type.

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Mathematics Subject Classification: 37A25, 37A05, 60G10.

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