Recurrence of integral zeros for ergodic flows

2024/12/04 by Ryzhikov, Valery V.
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.05326

Abstract

Let a flow T_t preserve an ergodic probability measure μ, ∫ f dμ=0, and μ(A)>0. Then for almost all x∈ A, for which f(x)≠ 0, there is a sequence t_k→ ∞ such that T_tkx∈ A and ∫₀^t_k f(T_sx)ds=0.

Related

• Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals
• Multiple ergodic averages for flows and an application
• Rank-one flows of transformations with infinite ergodic index
• An ergodic process of zero divergence-distance from its time-reversed process
• Polynomial bounds in the Ergodic Theorem for positive recurrent one-dimensional diffusions and integrability of hitting times