Flow equivalence of topological Markov shifts and Ruelle algebras
Kengo Matsumoto
TL;DR
This paper investigates the relationship between flow equivalence of topological Markov shifts and the conjugacy of actions on their associated Ruelle algebras, providing a new algebraic characterization.
Contribution
It introduces a novel characterization of flow equivalence using conjugacy of weighted actions on stabilized extended Ruelle algebras for Markov shifts.
Findings
Flow equivalence is characterized by conjugacy of certain actions.
Extended Ruelle algebras encode flow equivalence information.
The approach links dynamical systems with operator algebra structures.
Abstract
We study discrete flow equivalence of two-sided topological Markov shifts by using extended Ruelle algebras. We characterize flow equivalence of two-sided topological Markov shifts in terms of conjugacy of certain actions weighted by ceiling functions of two-dimensional torus on the stabilized extended Ruelle algebras for the Markov shifts.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology