Arithmetic isomorphism of hyperbolic toral automorphisms and sofic shifts
type: Item
instance of: scholarly article
title: Arithmetic isomorphism of hyperbolic toral automorphisms and sofic shifts
zbMATH Open document ID: 0810.58031
DOI: 10.1007/BF01075629
publication date: 1994-07-06T00:00:00Z
review text: Applying a new approach the author constructs for a hyperbolic automorphism \(T\) of the torus \(\mathbb{T}^ n\) (satisfying a few restrictions) a ``sofic'' compactum \(X\) and its continuous mapping onto the torus that is a bijection everywhere except a certain set of first Baire category. The mapping sends the shift to the automorphism \(T\), the semigroup of finite sequences to the semigroup of homoclinic points and tail partition with respect to the past and the future to the dilating and the contracting foliations, respectively.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 571841
zbMATH Keywords: \(n\)-dimensional torus
zbMATH Keywords: metric theory of dynamical systems
zbMATH Keywords: hyperbolic automorphism
author: A. M. Vershik
reviewed by: Yuri A. Brudnyi
MaRDI profile type: Publication
cites work: ENTROPY, A COMPLETE METRIC INVARIANT FOR AUTOMORPHISMS OF THE TORUS
cites work: Markov Partitions for Axiom A Diffeomorphisms
cites work: Smooth Markov partitions and toral automorphisms
cites work: Subshifts of finite type and sofic systems
cites work: Q4026492
full work available at URL: https://doi.org/10.1007/bf01075629
OpenAlex ID: W2015339826
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 571841