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 |
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Pages (from-to) | 2394-2416 |
Number of pages | 23 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 37 |
Issue number | 8 |
DOIs | |
State | Published - 1 Dec 2017 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics