Resolving extensions of finitely presented systems

Abstract

In this paper we extend certain central results of zero dimensional systems to higher dimensions. The first main result shows that if (Y,f) is a finitely presented system, then there exists a Smale space (X,F) and a u-resolving factor map $\pi_+: X\to Y$. If the finitely presented system is transitive, then we show there is a canonical minimal u-resolving Smale space extension. Additionally, we show that any finite-to-one factor map between transitive finitely presented systems lifts through u-resolving maps to an s-resolving map.