References & Citations
Mathematics > Dynamical Systems
Title: Correlations and ergodic averages for strongly and mildly mixing automorphisms
(Submitted on 21 Mar 2024 (v1), revised 23 Mar 2024 (this version, v2), latest version 28 Mar 2024 (v4))
Abstract: For a sequence $\psi(n)\to +0$ and a square-integrable nonzero function $f$ for typical mixing automorphisms $T$ the set $\{n:\, |(T^nf,f) |>\psi( n)\}$ is infinite. Mildly mixing automorphisms $T$ do not have convergence of nonzero averages $\frac 1 {k_n} \sum_{i=1}^{k_n}T^if (x)$ with the rate of $o\left(\frac 1 {k_n}\right)$.
Submission history
From: Valery V. Ryzhikov [view email][v1] Thu, 21 Mar 2024 17:41:03 GMT (17kb)
[v2] Sat, 23 Mar 2024 08:26:43 GMT (7kb)
[v3] Wed, 27 Mar 2024 09:15:48 GMT (7kb)
[v4] Thu, 28 Mar 2024 17:58:42 GMT (8kb)
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