# Ergodic properties of the ideal gas model for infinite billiards

## Repository of Nicolaus Copernicus University

 dc.contributor.author Frączek, Krzysztof dc.date.accessioned 2017-12-27T09:58:03Z dc.date.available 2017-12-27T09:58:03Z dc.date.issued 2017-12-27 dc.identifier.uri http://repozytorium.umk.pl/handle/item/4767 dc.description.abstract In this paper we study ergodic properties of the Poisson suspension (the ideal gas model) of the billiard flow $(b_t)_{t\in\mathbb R}$ on the plane with a $\Lambda$-periodic pattern ($\Lambda\subset\mathbb R^2$ is a lattice) of polygonal scatterers. We prove that if the billiard table is additionally rational then for a.e. direction $\theta\in S^1$ the Poisson suspension of the directional billiard flow $(b^\theta_t)_{t\in\mathbb R}$ is weakly mixing. This gives the weak mixing of the Poisson suspension of $(b_t)_{t\in\mathbb R}$. We also show that for a certain class of such rational billiards (including the periodic version of the classical wind-tree model) the Poisson suspension of $(b^\theta_t)_{t\in\mathbb R}$ is not mixing for a.e. $\theta\in S^1$. dc.description.sponsorship Narodowe Centrum Nauki grant 2014/13/B/ST1/03153 dc.language.iso eng dc.rights info:eu-repo/semantics/openAccess dc.subject ideal gas dc.subject Poisson suspension dc.subject rational billiards dc.subject periodic translation surfaces dc.subject weak mixing dc.subject mixing dc.title Ergodic properties of the ideal gas model for infinite billiards dc.type info:eu-repo/semantics/preprint
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