Deviations for generalized tiling billiards in cyclic polygons

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Bibliographic Details
Main Author:	Jay, Magali
Format:	Preprint
Published:	2024
Subjects:	Dynamical Systems 37E10, 37B10
Online Access:	Acceder al recurso
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_version_	1866911783715864576
author	Jay, Magali
author_facet	Jay, Magali
contents	This work continues the study of tiling billiards, a class of dynamical system introduced by Davis et al. in 2018. We develop the study of generalized tiling billiards in a cyclic polygon. This work shows that the behavior of generalized tiling billiards in cyclic N-gons with N > 4 is considerably different from that of triangular and quadrilateral tiling billiards studied before. Indeed, we exhibit an open set of generalized tiling billiard trajectories deviating sublinearly from their asymptotic direction, whereas for N = 3 or 4 almost every trajectory stays at a bounded distance from a line. Moreover, we establish the rate of deviations both in the generic case and in some non generic cases.
format	Preprint
id	arxiv_https___arxiv_org_abs_2402_15765
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Deviations for generalized tiling billiards in cyclic polygons Jay, Magali Dynamical Systems 37E10, 37B10 This work continues the study of tiling billiards, a class of dynamical system introduced by Davis et al. in 2018. We develop the study of generalized tiling billiards in a cyclic polygon. This work shows that the behavior of generalized tiling billiards in cyclic N-gons with N > 4 is considerably different from that of triangular and quadrilateral tiling billiards studied before. Indeed, we exhibit an open set of generalized tiling billiard trajectories deviating sublinearly from their asymptotic direction, whereas for N = 3 or 4 almost every trajectory stays at a bounded distance from a line. Moreover, we establish the rate of deviations both in the generic case and in some non generic cases.
title	Deviations for generalized tiling billiards in cyclic polygons
topic	Dynamical Systems 37E10, 37B10
url	https://arxiv.org/abs/2402.15765

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