Resolving extensions of finitely presented systems (Q368705)

In this paper the author extends certain central results of zero-dimensional systems (sofic shifts) to higher dimensions. The first main result shows that if \((Y, f)\) is a finitely presented system; that is, an expansive system which is a factor of a shift of finite type, then there exists a Smale space \((X,F)\); that is, an expansive system with canonical coordinates, and a \(u\)-resolving factor map \(\pi_+ : X \to Y\), which is injective on unstable sets. If the finitely presented system is transitive, then the author shows that there is a canonical minimal \(u\)-resolving Smale space extension. Moreover, the author shows that any finite-to-one factor map between transitive finitely presented systems lifts through \(u\)-resolving maps to an \(s\)-resolving map, which is a map injective on stable sets.