Ergodic properties of the ideal gas model for infinite billiards

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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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