Decay of correlations for billiards with flat points I: channel effects
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Publication:4686906
DOI10.1090/CONM/698/13984zbMATH Open1398.37015arXiv1605.06639OpenAlexW4236055275MaRDI QIDQ4686906
Author name not available (Why is that?)
Publication date: 10 October 2018
Published in: (Search for Journal in Brave)
Abstract: In this paper we constructed a special family of semidispersing billiards bounded on a rectangle with a few dispersing scatters. We assume there exists a pair of flat points (with zero curvature) on the boundary of these scatters, whose tangent lines form a channel in the billiard table that is perpendicular to the vertical sides of the rectangle. The billiard can be induced to a Lorenz gas with infinite horizon when replacing the rectangle by a torus. We study the mixing rates of the one-parameter family of the semi-dispersing billiards and the Lorenz gas on a torus; and show that the correlation functions of both maps decay polynomially.
Full work available at URL: https://arxiv.org/abs/1605.06639
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