Slow decay of correlations for generic mixing automorphisms
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866909153819099136 |
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| author | Ryzhikov, Valery V. |
| author_facet | Ryzhikov, Valery V. |
| contents | Let $ψ(n)\to +0$ and a square-integrable function $f$ be non-zero, then for the typical mixing automorphism $T$ the set $\{n:\, |(T^nf,f) |>ψ( n)\}$ is infinite. The mildly mixing automorphisms $T$ do not have convergences of non-zero averages $\frac 1 {k_n} \sum_{i=1}^{k_n}T^if (x)$ with the rate of $o\left(\frac 1 {k_n}\right)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Slow decay of correlations for generic mixing automorphisms Ryzhikov, Valery V. Dynamical Systems Let $ψ(n)\to +0$ and a square-integrable function $f$ be non-zero, then for the typical mixing automorphism $T$ the set $\{n:\, |(T^nf,f) |>ψ( n)\}$ is infinite. The mildly mixing automorphisms $T$ do not have convergences of non-zero averages $\frac 1 {k_n} \sum_{i=1}^{k_n}T^if (x)$ with the rate of $o\left(\frac 1 {k_n}\right)$. |
| title | Slow decay of correlations for generic mixing automorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2403.14585 |