TY - JOUR
T1 - Symmetric Birkhoff sums in infinite ergodic theory
AU - Aaronson, Jon
AU - Kosloff, Zemer
AU - Weiss, Benjamin
N1 - Publisher Copyright:
© Cambridge University Press, 2016.
PY - 2017/12/1
Y1 - 2017/12/1
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.
UR - http://www.scopus.com/inward/record.url?scp=84976877574&partnerID=8YFLogxK
U2 - 10.1017/etds.2016.18
DO - 10.1017/etds.2016.18
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AN - SCOPUS:84976877574
SN - 0143-3857
VL - 37
SP - 2394
EP - 2416
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 8
ER -