Ergodic behavior of graph entropy.
Ergodic properties of square-free numbers
We construct a natural invariant measure concentrated on the set of square-free numbers, and invariant under the shift. We prove that the corresponding dynamical system is isomorphic to a translation on a compact, Abelian group. This implies that this system is not weakly mixing and has zero measure-theoretical entropy.
Ergodic theorems for linear operators on with strict topology
Ergodic theorems for subadditive superstationary families of random sets with values in Banach spaces
Under different compactness assumptions pointwise and mean ergodic theorems for subadditive superstationary families of random sets whose values are weakly (or strongly) compact convex subsets of a separable Banach space are presented. The results generalize those of [14], where random sets in are considered. Techniques used here are inspired by [3].
Ergodic theory, entropy, and coding problems of information theory
Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval II
We construct examples of expanding piecewise monotonic maps on the interval which have a closed topologically transitive invariant subset A with Darboux property, Hausdorff dimension d ∈ (0,1) and zero d-dimensional Hausdorff measure. This shows that the results about Hausdorff and conformal measures proved in the first part of this paper are in some sense best possible.
Hausdorff and conformal measures for expanding piecewise monotonic maps of the interval
Let A be a topologically transitive invariant subset of an expanding piecewise monotonic map on [0,1] with the Darboux property. We investigate existence and uniqueness of conformal measures on A and relate Hausdorff and conformal measures on A to each other.
Hausdorff dimension for piecewise monotonic maps
Homogenization and ergodic theory
Individual ergodic theorem in a regular space
Intersecting random translates of invariant Cantor sets.
Invariant measures and a linear model of turbulence
Lemme de l'ombre et non divergence des horosphères d'une variété géométriquement finie
Dans cet article, nous établissons dans un premier temps un lemme de l'ombre dans le cas des variétés géométriquement finies à courbure négative variable. Ce théorème donne des estimées très précises de la décroissance de la mesure de Patterson des ombres, sur le bord à l'infini de telles variétés. Nous en déduisons un résultat de non divergence des horosphères. Plus précisément, nous considérons certaines moyennes naturelles sur de grandes boules horosphériques, dont nous...
On certain solutions of the diophantine equation x-y = p(z)
On certain weighted moving averages and their differentiation analogues.
On Exact Toral Endomorphisms.
On invariant elements for positive operators.
In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is...
On metric diophantine approximation and subsequence ergodic theory.
On subrelations of ergodic measured type III equivalence relations
We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.
On the individual ergodic theorem on a logic