Structure of eventual conjugacy of one-sided topological Markov shifts and isomorphisms of Cuntz–Krieger algebras

We will introduce the notion of lag map of one-sided topological Markov shifts to investigate eventual conjugacy of one-sided topological Markov shifts. We will then clarify structure of one-sided eventual conjugacy of topological Markov shifts from the three viewpoints: (1) isomorphisms of Cuntz–Krieger algebras, (2) homeomorphisms between one-sided topological Markov shifts, (3) matrix relations defining the eventual conjugate one-sided topological Markov shifts. As a result, we will characterize eventual conjugacy of one-sided topological Markov shifts in terms of the above three viewpoints by using lag maps.