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

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arxiv 2402.02266 v4 pith:CA5SBMQW submitted 2024-02-03 math.DS

Henk Bruin , Charles Fougeron , Davide Ravotti , Dalia Terhesiu This is my paper · ORCID
classification math.DS
keywords flowsself-similarergodicexpansionsextensionsintegralsobtaintranslation
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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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  1. Heat propagation on abelian covers of principal bundles

    math.AP 2026-08 conditional novelty 6.0 of 10

    Heat kernels on Abelian covers and their principal-bundle lifts share the same leading Gaussian large-time profile, with all polynomial coefficients determined by the base cover.

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