A period formula for torus automorphisms
type: Item
instance of: scholarly article
title: A period formula for torus automorphisms
zbMATH Open document ID: 1030.15017
author: Peter Seibt
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-02-18T00:00:00Z
review text: The paper determines the order of integer matrices \(A\in SL_2 (\mathbb{Z})\) on lattices \(L_N={1 \over N}\mathbb{Z}^2/ \mathbb{Z}^2\) of \(\mathbb{Q}^2/ \mathbb{Z}^2\), for \(N=P_n\equiv\) the number of \(n\)-periodic points (for the particular matrix-action on the rational 2-torus). The arguments lean heavily on arithmetical properties of (integer specializations of) certain Chebychev polynomials.
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 37E15
zbMATH DE Number: 1941563
zbMATH Keywords: discrete dynamical systems
zbMATH Keywords: finite orbit structure
zbMATH Keywords: torus automorphisms
zbMATH Keywords: periods of integer matrix actions
zbMATH Keywords: Chebychev polynomials
reviewed by: Rodica Covaci
MaRDI profile type: Publication
full work available at URL: dcds.2003.9.1029
OpenAlex ID: W2023133812
DOI: 10.3934/DCDS.2003.9.1029
description: scientific article; zbMATH DE number 1941563