Diffusion for the  periodic wind-tree model

Delecroix, Vincent; Hubert, Pascal; Lelièvre, Samuel

doi:10.24033/asens.2234

Diffusion for the periodic wind-tree model
[Diffusion du vent dans les arbres]

Delecroix, Vincent ; Hubert, Pascal ; Lelièvre, Samuel

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 6, pp. 1085-1110.

Résumé
Abstract

Le vent dans les arbres périodique est un billard infini construit de la manière suivante. On considère le plan dans lequel sont placés des obstacles rectangulaires identiques à chaque point entier. Une particule (identifiée à un point) se déplace en ligne droite (le vent) et rebondit de manière élastique sur les obstacles (les arbres). Nous prouvons qu'indépendamment de la taille des obstacles et génériquement par rapport à l'angle initial de la particule le coefficient de diffusion polynomial des orbites de ce billard est $2 / 3$ .

The periodic wind-tree model is an infinite billiard in the plane with identical rectangular scatterers placed at each integer point. We prove that independently of the size of scatters and generically with respect to the angle, the polynomial diffusion rate in this billiard is $2 / 3$ .

Publié le : 2014-11-18

MR Zbl | 1 citation dans Numdam

DOI : 10.24033/asens.2234

Classification : 30F30, 37E35, 37A40.
Keywords: Billiards, diffusion, translations surfaces, Lyapunov exponents, ergodic averages.
Mot clés : Billard, diffusion, surfaces de translation, exposants de Liapounoff, moyennes ergodiques.

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     author = {Delecroix, Vincent and Hubert, Pascal and Leli\`evre, Samuel},
     title = {Diffusion for the  periodic wind-tree model},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {1085--1110},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 47},
     number = {6},
     year = {2014},
     doi = {10.24033/asens.2234},
     mrnumber = {3297155},
     zbl = {1351.37159},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.2234/}
}

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Delecroix, Vincent; Hubert, Pascal; Lelièvre, Samuel. Diffusion for the  periodic wind-tree model. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 47 (2014) no. 6, pp. 1085-1110. doi : 10.24033/asens.2234. http://www.numdam.org/articles/10.24033/asens.2234/

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