Recurrence for the wind-tree model

Avila, A.; Hubert, P.

doi:10.1016/j.anihpc.2017.11.006

¹Universität Zürich, Institut für Mathematik, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
²IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil
³Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 1, pp. 1-11

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Résumé

In this paper, we give a geometric criterion ensuring the recurrence of the vertical flow on $Z^{d}$ -covers of compact translation surfaces ( $d \geq 2$ ). We prove that the linear flow in the wind-tree model is recurrent for every pair of parameters and almost every direction.

MR Zbl

DOI : 10.1016/j.anihpc.2017.11.006

Classification : 37C15, 37B10
Keywords: Polygonal billiards, Periodic translation surfaces, Recurrence

Affiliations des auteurs :

Avila, A. ^{1
,

2} ; Hubert, P. ³

¹ Universität Zürich, Institut für Mathematik, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
² IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil
³ Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France

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     title = {Recurrence for the wind-tree model},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1--11},
     year = {2020},
     publisher = {Elsevier},
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     number = {1},
     doi = {10.1016/j.anihpc.2017.11.006},
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     zbl = {1436.37006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.11.006/}
}

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Avila, A.; Hubert, P. Recurrence for the wind-tree model. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 1, pp. 1-11. doi: 10.1016/j.anihpc.2017.11.006

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