Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we investigate their almost isomorphism and entropy conjugacy and obtain a complete classification for the especially important… (More)
We show that a class of robustly transitive diffeomor-phisms originally described by Mañé are intrinsically ergodic. More precisely, we obtain an open set of diffeomorphisms which fail to be uniformly hyperbolic and structurally stable, but nevertheless have the following stability with respect to their entropy. Their topological entropy is constant and… (More)
We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems , e.g., piecewise monotonic maps of the interval with positive entropy. Yet many properties remain: existence of finitely many ergodic… (More)
We show that a class of robustly transitive diffeomor-phisms originally described by Mañé are intrinsically ergodic. More precisely, we obtain an open set of diffeomorphisms which fail to be uniformly hyperbolic and structurally stable, but nevertheless have constant entropy and isomorphic unique measures of maximal entropy.
We study the dynamics of piecewise affine surface homeomor-phisms from the point of view of their entropy. Under the assumption of positive topological entropy, we establish the existence of finitely many ergodic and invariant probability measures maximizing entropy and prove a multiplicative lower bound for the number of periodic points. This is intended… (More)
— We give a survey of the entropy theory of interval maps as it can be analyzed using ergodic theory, especially measures of maximum entropy and periodic points. The main tools are (i) a suitable version of Hofbauer's Markov diagram, (ii) the shadowing property and the implied entropy bound and weak rank one property, (iii) strongly positively recurrent… (More)