The Abramov-Rokhlin Entropy Addition Formula for Amenable Group Actions.
The Box Dimension of Completely Invariant Subsets for Expanding Piecewise Monotonic Transformations.
The capacity of parabolic Julia sets.
The Dynamical Complexity of Orientation Reversing Homeomorphisms of Surfaces.
The dynamics of piecewise monotonic maps under small perturbations
The entropy function on an algebraic structure with infinite partition and -preserving transformation generators.
The entropy on -quantum spaces
The ergodic theory of shrinking targets.
The finitary isomorphism problem for one-dimensional Gibbs systems of molecular type
The Geometry of Model Spaces for Probability-Preserving Actions of Sofic Groups
Bowen’s notion of sofic entropy is a powerful invariant for classifying probability-preserving actions of sofic groups. It can be defined in terms of the covering numbers of certain metric spaces associated to such an action, the ‘model spaces’. The metric geometry of these model spaces can exhibit various interesting features, some of which provide other invariants of the action. This paper explores an approximate connectedness property of the model spaces, and uses it give a new proof that certain...
The Poisson formula for groups with hyperbolic properties.
The sequence entropy for Morse shifts and some counterexamples
Théorie ergodique : classification de certaines transformations réelles
Topological Markov chains with dicyclic dimension group.
Topological Pressure for One-Dimensional Holomorphic Dynamical Systems
For a class of one-dimensional holomorphic maps f of the Riemann sphere we prove that for a wide class of potentials φ the topological pressure is entirely determined by the values of φ on the repelling periodic points of f. This is a version of a classical result of Bowen for hyperbolic diffeomorphisms in the holomorphic non-uniformly hyperbolic setting.