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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.13486 |
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| _version_ | 1866915047405518848 |
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| author | Ryzhikov, Valery V. |
| author_facet | Ryzhikov, Valery V. |
| contents | We recall theorems by Krygin, Atkinson, Shneiberg and propose the following assertion. Let $T_t$ be an ergodic flow on $(X,μ)$, let a function $f$ on $X$ have zero mean, and $μ(A)>0$ for $A\subset X$. Then for almost all $x\in A$ with $f(x)\neq 0$ there exists a sequence $t_k\to\infty$ such that $\int_0^{t_k}f(T_sx)ds=0$ and $T_{t_k}x\in A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13486 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals Ryzhikov, Valery V. Dynamical Systems We recall theorems by Krygin, Atkinson, Shneiberg and propose the following assertion. Let $T_t$ be an ergodic flow on $(X,μ)$, let a function $f$ on $X$ have zero mean, and $μ(A)>0$ for $A\subset X$. Then for almost all $x\in A$ with $f(x)\neq 0$ there exists a sequence $t_k\to\infty$ such that $\int_0^{t_k}f(T_sx)ds=0$ and $T_{t_k}x\in A$. |
| title | Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2411.13486 |