On quadrilateral orbits in planar billiards
type: Item
instance of: scholarly article
title: On quadrilateral orbits in planar billiards
zbMATH Open document ID: 1238.37010
DOI: 10.1134/S1064562411030343
author: Yu. G. Kudryashov
author: Alexey A. Glutsyuk
published in: Doklady Mathematics
publication date: 2012-01-17T00:00:00Z
review text: The authors state several results in the direction of Ivrii's conjecture which asserts that the set of periodic billiard orbits in a domain \(\Omega\subset {\mathbb R}^m\) has measure zero in the space of all billiard trajectories, assuming that the boundary \(\partial \Omega\) is sufficiently smooth. One of the main results of the paper states that for any planar billiard domain with piecewise analytic boundary the set \(\text{Per}_4\) has no interior points.
Mathematics Subject Classification ID: 37D50
zbMATH DE Number: 5998413
zbMATH Keywords: billiards
zbMATH Keywords: periodic billiard trajectories
zbMATH Keywords: Ivrii's conjecture
reviewed by: Michael Farber
MaRDI profile type: Publication
cites work: Second term of the spectral asymptotic expansion of the Laplace-Beltrami operator on manifolds with boundary
cites work: Periodic points of the billiard ball map in a convex domain
cites work: On the measure of the set of periodic points of the billiard
full work available at URL: s1064562411030343
OpenAlex ID: W2049146510
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description: scientific article; zbMATH DE number 5998413