Recurrence of integral zeros for ergodic flows

Valery V. Ryzhikov

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arXiv · 2412.05326

Recurrence of integral zeros for ergodic flows

Valery V. Ryzhikov

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Abstract

Let a flow $T_t$ preserve an ergodic probability measure $\mu$, $\int f\,d\mu=0$, and $\mu(A)>0$. 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 $\int_0^{t_k} f(T_sx)ds=0$.

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BibTeX RIS

Valery V. Ryzhikov. 2024-12-04. Recurrence of integral zeros for ergodic flows. https://arxiv.org/abs/2412.05326

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