Geodesic
Slow Convergences of Ergodic Averages
Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 742-746

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Birkhoff's theorem asserts that, for an ergodic automorphism, time averages converge to the space average. Krengel showed that, for a given sequence $\psi(n)\to+0$ and any ergodic automorphism, there exists an indicator function such that the corresponding time means converge a.e. slower than $\psi$. We give a new proof of the absence of estimates for rates of convergence, answering a question of Podvigin.
Keywords: ergodic averages, convergence almost everywhere, rate of convergence.
Mots-clés : convergence in norm 
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     author = {V. V. Ryzhikov},
     title = {Slow {Convergences} of {Ergodic} {Averages}},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
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V. V. Ryzhikov. Slow Convergences of Ergodic Averages. Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 742-746. http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a9/