Arithmetic isomorphism of hyperbolic toral automorphisms and sofic shifts
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.
scientific article; zbMATH DE number 571841