Symmetric Birkhoff sums in infinite ergodic theory

Jon Aaronson; Zemer Kosloff; Benjamin Weiss

doi:https://doi.org/10.1017/etds.2016.18

Symmetric Birkhoff sums in infinite ergodic theory

Jon Aaronson, Zemer Kosloff, Benjamin Weiss

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2394-2416
Number of pages	23
Journal	Ergodic Theory and Dynamical Systems
Volume	37
Issue number	8
DOIs	https://doi.org/10.1017/etds.2016.18
State	Published - 1 Dec 2017

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "Symmetric Birkhoff sums in infinite ergodic theory",

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.",

author = "Jon Aaronson and Zemer Kosloff and Benjamin Weiss",

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AU - Kosloff, Zemer

AU - Weiss, Benjamin

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N2 - 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.

AB - 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.

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U2 - https://doi.org/10.1017/etds.2016.18

DO - https://doi.org/10.1017/etds.2016.18

M3 - مقالة

SN - 0143-3857

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JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 8

ER -

Symmetric Birkhoff sums in infinite ergodic theory

Abstract

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