On the measure of the set of periodic points of the billiard
type: Item
instance of: scholarly article
title: On the measure of the set of periodic points of the billiard
zbMATH Open document ID: 0838.58032
DOI: 10.1007/BF02110371
author: Ya. B. Vorobets
published in: Mathematical Notes
publication date: 1995-09-25T00:00:00Z
review text: Let \(G\) be a bounded domain in \(\mathbb{R}^n\) \((n\geq 2)\) and let \(T\) denote the Poincaré map of the billiard flow on \(G\) defined by hitting the boundary of \(G\). It is shown that the set of \(T\)-periodic points of period 3 has Lebesgue measure zero.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 797884
zbMATH Keywords: periodic points
zbMATH Keywords: Poincaré map
zbMATH Keywords: billiard flow
zbMATH Keywords: Lebesgue measure zero
reviewed by: Manfred Denker
MaRDI profile type: Publication
cites work: Periodic points of the billiard ball map in a convex domain
cites work: Note on the periodic points of the billiard
description: scientific article; zbMATH DE number 797884