On asymptotic expansions of ergodic integrals for \Z^d-extensions of translation flows

2024/02/03 by Henk Bruin, Charles Fougeron, Bruin, Henk +5 · 3 citations
Economics, Econometrics and Finance · Mathematics · #14H30 #37H05 #60F15 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 37E35 #Secondary 28D05 #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2402.02266

openalex publication_date 2024/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain expansions of ergodic integrals for \Z^d-covers of compact self-similar translation flows, and as a consequence we obtain a form of weak rational ergodicity with optimal rates. As examples, we consider the so-called self-similar (s,1)-staircase flows (\Z-extensions of self-similar translations flows of genus-2 surfaces), and particular cases of the Ehrenfest wind-tree model.

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