Related papers: Strongly continuous orbit equivalence of one-sided…
We will prove that one-sided topological Markov shifts $(X_A,\sigma_A)$ and $(X_B,\sigma_B)$ for matrices $A$ and $B$ with entries in $\{0,1\}$ are topologically orbit equivalent if and only if there exists an isomorphism between the…
For continuously orbit equivalent one-sided topological Markov shifts $(X_A,\sigma_A)$ and $(X_B,\sigma_B)$, their eventually periodic points and cocycle functions are studied. As a result we directly construct an isomorphism between their…
Let A,B be square irreducible matrices with entries in {0,1}. We will show that if the one-sided topological Markov shifts (X_A,\sigma_A) and (X_B,\sigma_B) are continuously orbit equivalent, then the two-sided topological Markov shifts…
We introduce a notion of uniformly continuous orbit equivalence as a subequivalence relation of continuous orbit equivalence of one-sided topological Markov shifts. It is described in terms of gauge actions on the associated Cuntz-Krieger…
We introduce a notion of coded equivalence in one-sided topological Markov shifts. The notion is inspired by coding theory. One-sided topological conjugacy implies coded equivalence. We will show that coded equivalence implies continuous…
We will study several subgroups of continuous full groups of one-sided topological Markov shifts from the view points of cohomology groups of full group actions on the shift spaces. We also study continuous orbit equivalence and strongly…
We study KMS states for gauge actions with potential functions on Cuntz--Krieger algebras whose underlying one-sided topological Markov shifts are continuous orbit equivalent. As a result, we have a certain relationship between topological…
We take the first steps towards a better understanding of continuous orbit equivalence, i.e., topological orbit equivalence with continuous cocycles. First, we characterise continuous orbit equivalence in terms of isomorphisms of C*-crossed…
We give conditions for when continuous orbit equivalence of one-sided shift spaces implies flow equivalence of the associated two-sided shift spaces. Using groupoid techniques, we prove that this is always the case for shifts of finite…
Let $(X_A,\sigma_A)$ be the right one-sided topological Markov shift for an irreducible matrix with entries in $\{0,1\}$, and $\Gamma_A$ the continuous full group of $(X_A,\sigma_A)$. For two irreducible matrices $A$ and $B$ with entries in…
We study asymptotic continuous orbit equivalence of Smale spaces. We prove that two irreducible Smale spaces are flip conjugate if and only if there exists a periodic point preserving homeomorphism giving an asymptotic continuous orbit…
We study the notions of continuous orbit equivalence and eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graphs with finitely many vertices and no sinks or sources. We…
We will characterize topological conjugate one-sided topological Markov shifts in terms of their subgroups of continuous full groups and subalgebras of Cuntz--Krieger algebras.
We introduce notions of continuous orbit equivalence and strong (respective, weak) continuous orbit equivalence for automorphism systems of \'{e}tale equivalence relations, and characterize them in terms of the semi-direct product…
To every one-sided shift space $\mathsf{X}$ we associate a cover $\tilde{\mathsf{X}}$, a groupoid $\mathcal{G}_{\mathsf{X}}$ and a $\mathrm{C^*}$-algebra $\mathcal{O}_{\mathsf{X}}$. We characterize one-sided conjugacy, eventual conjugacy…
We introduce notions of suspension and flow equivalence on one-sided topological Markov shifts, which we call one-sided suspension and one-sided flow equivalence, respectively. We prove that one-sided flow equivalence is equivalent to…
We introduce and study a unital version of shift equivalence for finite square matrices over the nonnegative integers. In contrast to the classical case, we show that unital shift equivalence does not coincide with one-sided eventual…
We will characterize topologically conjugate two-sided topological Markov shifts $(\bar{X}_A,\bar{\sigma}_A)$ in terms of the associated asymptotic Ruelle $C^*$-algebras ${\mathcal{R}}_A$ with its commutative $C^*$-subalgebras…
A $\lambda$-graph system ${\frak L}$ is a generalization of a finite labeled graph and presents a subshift. We will prove that the topological dynamical systems $(X_{{\frak L}_1},\sigma_{{\frak L}_1})$ and $(X_{{\frak L}_2},\sigma_{{\frak…
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…