Description of sequences defined by billiards in the cube
type: Item
instance of: scholarly article
title: Description of sequences defined by billiards in the cube
zbMATH Open document ID: 0773.11020
author: Iekata Shiokawa
author: Jun-ichi Tamura
published in: Proceedings of the Japan Academy. Series A
publication date: 1993-06-29T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pja/1195511709
review text: A billiard game in the 3-dimensional cube is considered. The orbit of a lattice-free point can be encoded as a sequence with three symbols. In a preceding paper by \textit{K. Nishioka}, \textit{I. Shiokawa} and \textit{J. Tamura} [J. Number Theory 42, 61--87 (1992; Zbl 0770.11039)] an algorithm for the description of an admissible sequence was given. In the present paper another description is given which uses continued fractions and a related series expansion.
reviewed by: Fritz Schweiger
Mathematics Subject Classification ID: 11B05
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 37D50
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 221216
zbMATH Keywords: topological dynamics
zbMATH Keywords: billiard
zbMATH Keywords: lattice-free point
zbMATH Keywords: algorithm
zbMATH Keywords: continued fractions
MaRDI profile type: Publication
OpenAlex ID: W2048583413
cites work: Arithmetical properties of a certain power series
cites work: Beatty Sequences, Continued Fractions, and Certain Shift Operators
DOI: 10.3792/PJAA.68.207
description: scientific article; zbMATH DE number 221216