Espaces fonctionnels et théorèmes de I. Namioka
Estimates of capacity of self-similar measures
We give lower and upper estimates of the capacity of self-similar measures generated by iterated function systems where are bi-lipschitzean transformations.
Estimations de la dimension inférieure et de la dimension supérieure des mesures
Etude spectrale des substitutions de longueur constante
Exactness of expanding mappings
Existence of discrete ergodic singular transforms for admissible processes
This article is concerned with the study of the discrete version of generalized ergodic Calderón-Zygmund singular operators. It is shown that such discrete ergodic singular operators for a class of superadditive processes, namely, bounded symmetric admissible processes relative to measure preserving transformations, are weak (1,1). From this maximal inequality, a.e. existence of the discrete ergodic singular transform is obtained for such superadditive processes. This generalizes the well-known...
Existence of invariant measures for piecewise continuous transformations
Existence of time averages from the topological point of view
Explicit construction of normal lattice configurations
We extend Champernowne’s construction of normal numbers to base b to the case and obtain an explicit construction of a generic point of the shift transformation of the set .
Extending quasi-invariant measures by using subgroups of a given group.
Extension of the Birkhoff and von Neumann ergodic theorems to semigroup actions
Extensions de systèmes dynamiques par des endomorphismes de groupes compacts
Extensions of Cocycles for Hyperfinite Actions and Applications.
Extensions of probability-preserving systems by measurably-varying homogeneous spaces and applications
We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such extensions rests on a simple notion of 'direct integral' for a 'measurable family' of homogeneous spaces, which has a number of precedents in older literature. The main contribution of the present paper is the systematic development of a formalism for handling such extensions,...
Factors and Extensions of Full Shifts.
Factors of coalescent automorphisms
Factors of ergodic group extensions of rotations
Diagonal metric subgroups of the metric centralizer of group extensions are investigated. Any diagonal compact subgroup Z of is determined by a compact subgroup Y of a given metric compact abelian group X, by a family , of group automorphisms and by a measurable function f:X → G (G a metric compact abelian group). The group Z consists of the triples , y ∈ Y, where , x ∈ X.
Faithful zero-dimensional principal extensions
We prove that every topological dynamical system (X,T) has a faithful zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν | X) is zero, and, in addition, every invariant measure on X has exactly one preimage on Y. This is a strengthening of the authors' result in Acta Appl. Math. [to appear] (where the extension was principal, but not necessarily faithful).
Fibrés dynamiques. Entropie et dimension
Finitarily Bernoulli factors are dense
It is not known if every finitary factor of a Bernoulli scheme is finitarily isomorphic to a Bernoulli scheme (is finitarily Bernoulli). In this paper, for any Bernoulli scheme X, we define a metric on the finitary factor maps from X. We show that for any finitary map f: X → Y, there exists a sequence of finitary maps fₙ: X → Y(n) that converges to f, where each Y(n) is finitarily Bernoulli. Thus, the maps to finitarily Bernoulli factors are dense. Let (X(n)) be a sequence of Bernoulli schemes such...