Symmetries and reversing symmetries of toral automorphisms (Q2732651)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Symmetries and reversing symmetries of toral automorphisms |
scientific article; zbMATH DE number 1624842
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Symmetries and reversing symmetries of toral automorphisms |
scientific article; zbMATH DE number 1624842 |
Statements
Symmetries and reversing symmetries of toral automorphisms (English)
0 references
28 August 2002
0 references
toral automorphism
0 references
symmetry
0 references
0.9015088
0 references
0.8974017
0 references
0.89734566
0 references
0 references
0.89495355
0 references
0.88859206
0 references
0 references
0.88055253
0 references
0.8804943
0 references
The well-known connection between integer matrices with simple spectrum and unit groups in orders of algebraic number fields is used to describe the structure of the toral automorphisms \(F\) that are symmetries of \(G\) (that is, \(FG=GF\)) or are reversing symmetries (that is \(FG=G^{-1}F\)). The rather complete classification available for the 2-torus is extended to the \(n\)-torus here. As the authors point out, the methods used are quite standard in number theory, but are not perhaps widely known in the dynamical systems community.
0 references
