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Joint ergodicity along generalized linear functions

Published online by Cambridge University Press:  15 June 2015

V. BERGELSON ,
A. LEIBMAN  and
Y. SON
V. BERGELSON
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA email [email protected], [email protected]
A. LEIBMAN
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA email [email protected], [email protected]
Y. SON
Affiliation:
Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, 234 Herzl Street, Rehovot 7610001, Israel email [email protected]
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Abstract

A criterion of joint ergodicity of several sequences of transformations of a probability measure space $X$ of the form $T_{i}^{\unicode[STIX]{x1D711}_{i}(n)}$ is given for the case where $T_{i}$ are commuting measure-preserving transformations of $X$ and $\unicode[STIX]{x1D711}_{i}$ are integer-valued generalized linear functions, that is, the functions formed from conventional linear functions by an iterated use of addition, multiplication by constants, and the greatest integer function. We also establish a similar criterion for joint ergodicity of families of transformations depending on a continuous parameter, as well as a condition of joint ergodicity of sequences $T_{i}^{\unicode[STIX]{x1D711}_{i}(n)}$ along primes.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 7 , October 2016 , pp. 2044 - 2075
Copyright
© Cambridge University Press, 2015 

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