Recurrence for the wind-tree model

  • A. Avila

    Universität Zürich, Institut für Mathematik, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland, IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil
  • P. Hubert

    Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
Recurrence for the wind-tree model cover
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In this paper, we give a geometric criterion ensuring the recurrence of the vertical flow on -covers of compact translation surfaces (). We prove that the linear flow in the wind-tree model is recurrent for every pair of parameters and almost every direction.

Cite this article

A. Avila, P. Hubert, Recurrence for the wind-tree model. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 1, pp. 1–11

DOI 10.1016/J.ANIHPC.2017.11.006