We show that symbolic finite-to-one extensions of the type constructed by O. Sarig for surface diffeomorphisms induce H\"older-continuous conjugacies on large sets, sometimes preserving transitivity. We deduce this from their Bowen property. This notion, introduced in a joint work with M. Boyle, generalizes a fact first observed by R. Bowen for Markov partitions. We use the notion of degree from finite equivalence theory and magic word isomorphisms. As an application, we improve Sarig's lower bound on the number of periodic points for surface diffeomorphisms. Finally we characterize surface diffeomorphisms admitting a H\"older-continuous coding of all their aperiodic hyperbolic measures. 查看全文>>