Slow decay of correlations for generic mixing automorphisms

2024/03/21 by Ryzhikov, Valery V.
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.14585

Abstract

Let ψ(n)→ +0 and a square-integrable function f be non-zero, then for the typical mixing automorphism T the set \n: |(Tⁿf,f) |>ψ( n)\ is infinite. The mildly mixing automorphisms T do not have convergences of non-zero averages \frac 1 k_n ∑_i=1^k_nTⁱf (x) with the rate of o(\frac 1 k_n).

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