2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134413We will prove that one-sided topological Markov shifts $(X_A,σ_A)$ and $(X_B,σ_B)$ for matrices $A$ and $B$ with entries in $\{0,1\}$ are topologically orbit equivalent if and only if there exists an isomorphism between the Cuntz-Krieger algebras ${\Cal O}_A$ and ${\Cal O}_B$ keeping their commutative $C^*$-subalgerbas $C(X_A)$ and $C(X_B)$. It is also equivalent to the condition that there exists a homeomorphism from $X_A$ to $X_B$ intertwining their topological full groups. We will also study structure of the automorphisms of ${\Cal O}_A$ keeping the commutative $C^*$-algebra $C(X_A)$.26 pagesOperator AlgebrasDynamical Systems46L55text