Arithmetical properties of strongly chaotic motions
type: Item
instance of: scholarly article
title: Arithmetical properties of strongly chaotic motions
zbMATH Open document ID: 0616.58039
DOI: 10.1016/0167-2789(87)90096-0
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: The authors use techniques of algebraic number theory to interpret periodic orbits on the 2-torus which result from hyperbolic automorphisms (as special case of Anosov diffeomorphisms) [see \textit{Ya. G. Sinai}, Introduction to ergodic theory (1976; Zbl 0375.28011)]. Orbits of points which generate prime ideals as lattice vectors are of particular interest, and applications are found for the matrix representations of ideals [see the reviewer, A classical invitation to algebraic numbers and class fields, and the Appendix by \textit{O. Taussky}, Introduction to connections between algebraic number theory and integral matrices (1978; Zbl 0395.12001)].
reviewed by: Harvey Cohn
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 3998839
zbMATH Keywords: torus automorphisms
zbMATH Keywords: matrix representations
zbMATH Keywords: Anosov diffeomorphisms
zbMATH Keywords: algebraic number theory
zbMATH Keywords: periodic orbits
zbMATH Keywords: hyperbolic automorphisms
author: Ian C. Percival
author: Franco Vivaldi
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90096-0
OpenAlex ID: W2068654798
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cites work: Solitons and condensed matter physics. Proceedings of the symposium on nonlinear (soliton) structure and dynamics in condensed matter. Oxford, England, June 27-29, 1978
description: scientific article; zbMATH DE number 3998839