On the positivity of an invariant measure on open non-empty sets
On the statistical properties of ergodic economic systems.
On the uniqueness of equilibrium states for piecewise monotone mappings
Parabolic Cantor sets
The notion of a parabolic Cantor set is introduced allowing in the definition of hyperbolic Cantor sets some fixed points to have derivatives of modulus one. Such difference in the assumptions is reflected in geometric properties of these Cantor sets. It turns out that if the Hausdorff dimension of this set is denoted by h, then its h-dimensional Hausdorff measure vanishes but the h-dimensional packing measure is positive and finite. This latter measure can also be dynamically characterized as the...
Periodic points and rotation numbers for area preserving diffeomorphisms of the plane
Persistent rotation intervals for old maps
Poincaré's recurrence theorem for set-valued dynamical systems
Abstract. The existence theorem of an invariant measure and Poincare's Recurrence Theorem are extended to set-valued dynamical systems with closed graph on a compact metric space.
Positive measure sets of ergodic rational maps
Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés
Pseudo-Markov transformations
Random dynamics and its applications.
Rate of convergence of conditional entropies for some maps of an interval
Regularity of measure theoretic entropy for geodesic flows of negative curvature: I.
Regularity of topological and metric entropy of hyperbolic flows.
Relating Hausdorff measures and harmonic measures on parabolic Jordan curves.
Rigid reparametrizations and cohomology for horocycle flows.
Rigidity and inflexibility in conformal dynamics.
Rotation sets and ergodic measures for torus homeomorphisms
Rotation sets for subshifts of finite type
For a dynamical system (X,f) and a function the rotation set is defined. The case when (X,f) is a transitive subshift of finite type and φ depends on the cylinders of length 2 is studied. Then the rotation set is a convex polyhedron. The rotation vectors of periodic points are dense in the rotation set. Every interior point of the rotation set is a rotation vector of an ergodic measure.
Self-Similar Sets 3. Constructions with Sofic Systems.