Visualizing toral automorphisms
type: Item
instance of: scholarly article
title: Visualizing toral automorphisms
zbMATH Open document ID: 0772.57035
DOI: 10.1007/BF03025260
author: Matthew A. Grayson
author: George Zettler
author: Bruce Kitchens
published in: The Mathematical Intelligencer
publication date: 1993-05-16T00:00:00Z
review text: The group of continuous automorphisms on the torus is isomorphic to \(\text{GL}(2,\mathbb{Z})\). Picture a torus constructed by joining two tubes of different colors. Figures show the mixing of the colors as the automorphism \({{2\;1}\choose {1\;1}}\) is iterated. A variety of properties of toral automorphisms are described and how to visualize them geometrically. The interested reader is encouraged to look at the pictures, they are worth more than a thousand words.
Mathematics Subject Classification ID: 57R50
Mathematics Subject Classification ID: 00A08
zbMATH DE Number: 168570
zbMATH Keywords: automorphisms
zbMATH Keywords: torus
reviewed by: George E. Lang jun.
MaRDI profile type: Publication
cites work: Ergodic automorphisms of \(T^ n\) are Bernoulli shifts
cites work: The existence of expansive homeomorphisms on manifolds
cites work: Q5508728
cites work: Similarity of automorphisms of the torus
cites work: Homeomorphic conjugacy of automorphisms on the torus
description: scientific article; zbMATH DE number 168570