Residual entropy, conditional entropy and subshift covers

We study the existence of subshift covers for topological dynamical systems, the infimum of the entropy jumps to such covers, and various aspects of conditional entropy and covering maps including a variational principle for covering maps. In particular we show every asymptotically h-expansive system (and therefore by Buzzi every C-infinity homeomorphism of a compact Riemannian manifold) has a subshift cover of equal entropy. Our arguments in dimension zero are extended to higher dimension with theorems of Kulesza and Thomsen.