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Symmetric Birkhoff sums in infinite ergodic theory

Published online by Cambridge University Press:  04 July 2016

JON AARONSON ,
ZEMER KOSLOFF  and
BENJAMIN WEISS
JON AARONSON
Affiliation:
School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel email [email protected]
ZEMER KOSLOFF
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK email [email protected]
BENJAMIN WEISS
Affiliation:
Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904, Israel email [email protected]
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Abstract

We show that the absolutely normalized, symmetric Birkhoff sums of positive integrable functions in infinite, ergodic systems never converge pointwise even though they may be almost surely bounded away from zero and infinity. Also, we consider the latter phenomenon and characterize it among transformations admitting generalized recurrent events.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 8 , December 2017 , pp. 2394 - 2416
Copyright
© Cambridge University Press, 2016 

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