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Article contents
Binary factors of shifts of finite type
Part of:
Dynamical systems with hyperbolic behavior
Selfadjoint operator algebras
Topological dynamics
Published online by Cambridge University Press: 18 April 2023
Abstract
We construct two new classes of topological dynamical systems; one is a factor of a one-sided shift of finite type while the second is a factor of the two-sided shift. The data are a finite graph which presents the shift of finite type, a second finite directed graph and a pair of embeddings of it into the first, satisfying certain conditions. The factor is then obtained from a simple idea based on binary expansion of real numbers. In both cases, we construct natural metrics on the factors and, in the second case, this makes the system a Smale space, in the sense of Ruelle. We compute various algebraic invariants for these systems, including the homology for Smale space developed by the author and the K-theory of various 
$C^{*}$-algebras associated to them, in terms of the pair of original graphs.
MSC classification
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press
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