Article Dans Une Revue Studia Mathematica Année : 2025

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

Résumé

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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hal-05396635 , version 1 (03-12-2025)

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Henk Bruin, Charles Fougeron, Davide Ravotti, Dalia Terhesiu. On asymptotic expansions of ergodic integrals for Z d -extensions of translation flows. Studia Mathematica, 2025, 284, pp.229-280. ⟨10.4064/sm240425-15-4⟩. ⟨hal-05396635⟩
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