Recurrence of integral zeros for ergodic flows
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909471724273664 |
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| author | Ryzhikov, Valery V. |
| author_facet | Ryzhikov, Valery V. |
| contents | Let a flow $T_t$ preserve an ergodic probability measure $μ$, $\int f\,dμ=0$, and $μ(A)>0$. Then for almost all $x\in A$, for which $f(x)\neq 0$, there is a sequence ${t_k}\to \infty$ such that $T_{t_k}x\in A$ and $\int_0^{t_k} f(T_sx)ds=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05326 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recurrence of integral zeros for ergodic flows Ryzhikov, Valery V. Dynamical Systems Let a flow $T_t$ preserve an ergodic probability measure $μ$, $\int f\,dμ=0$, and $μ(A)>0$. Then for almost all $x\in A$, for which $f(x)\neq 0$, there is a sequence ${t_k}\to \infty$ such that $T_{t_k}x\in A$ and $\int_0^{t_k} f(T_sx)ds=0$. |
| title | Recurrence of integral zeros for ergodic flows |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2412.05326 |