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Arithmetic isomorphism of hyperbolic toral automorphisms and sofic shifts. (English. Russian original) Zbl 0810.58031

Funct. Anal. Appl. 26, No. 3, 170-173 (1992); translation from Funkts. Anal. Prilozh. 26, No. 3, 22-27 (1992).
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.

MSC:

37D99 Dynamical systems with hyperbolic behavior
28D05 Measure-preserving transformations
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