Ratio limit theorems and applications to ergodic theory
Rectangle Exchange Transformations.
Refinement of the Shannon-McMillan-Breiman theorem for some maps of an interval
Reformulation et extension de certains théorèmes ergodiques
Relating Hausdorff measures and harmonic measures on parabolic Jordan curves.
Relations between Shy Sets and Sets of -Measure Zero in Solovay’s Model
An example of a non-zero non-atomic translation-invariant Borel measure on the Banach space is constructed in Solovay’s model. It is established that, for 1 ≤ p < ∞, the condition "-almost every element of has a property P" implies that “almost every” element of (in the sense of [4]) has the property P. It is also shown that the converse is not valid.
Remark on BV-solutions of a functional equation connected with invariant measures.
Remarks on a Lemma in Ergodic Theory.
Remarks on the tightness of cocycles
We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.
Représentation géométrique de suites de complexité
Représentation intégrale de certaines mesures quasi-invariantes sur ; mesures extrémales et propriété de Markov
On établit pour le cône des mesures positives bornées sur , quasi-invariantes sous les translations de et vérifiant :(avec polynôme borné inférieurement) les résultats suivants :– Toute mesure de est intégrale de mesures appartenant aux génératrices extrémales de .– Les génératrices extrémales de sont composées de mesures markoviennes.
Résolution d'une équation fonctionnelle
Rigidity and cocycles for ergodic actions of semi-simple Lie groups
Ruelle operator with nonexpansive IFS
The Ruelle operator and the associated Perron-Frobenius property have been extensively studied in dynamical systems. Recently the theory has been adapted to iterated function systems (IFS) , where the ’s are contractive self-maps on a compact subset and the ’s are positive Dini functions on X [FL]. In this paper we consider Ruelle operators defined by weakly contractive IFS and nonexpansive IFS. It is known that in such cases, positive bounded eigenfunctions may not exist in general. Our theorems...
Sections in function spaces
Self-Similar Sets 3. Constructions with Sofic Systems.
Semisimplicity, joinings and group extensions
We present a theory of self-joinings for semisimple maps and their group extensions which is a unification of the following three cases studied so far: (iii) Gaussian-Kronecker automorphisms: [Th], [Ju-Th]. (ii) MSJ and simple automorphisms: [Ru], [Ve], [Ju-Ru]. (iii) Group extension of discrete spectrum automorphisms: [Le-Me], [Le], [Me].
Sequence entropy pairs and complexity pairs for a measure
In this paper we explore topological factors in between the Kronecker factor and the maximal equicontinuous factor of a system. For this purpose we introduce the concept of sequence entropy -tuple for a measure and we show that the set of sequence entropy tuples for a measure is contained in the set of topological sequence entropy tuples [H- Y]. The reciprocal is not true. In addition, following topological ideas in [BHM], we introduce a weak notion and a strong notion of complexity pair for a...
Sets with doubleton sections, good sets and ergodic theory
A Borel subset of the unit square whose vertical and horizontal sections are two-point sets admits a natural group action. We exploit this to discuss some questions about Borel subsets of the unit square on which every function is a sum of functions of the coordinates. Connection with probability measures with prescribed marginals and some function algebra questions is discussed.
Shift invariant measures and simple spectrum
We consider some descriptive properties of supports of shift invariant measures on under the assumption that the closed linear span (in ) of the co-ordinate functions on is all of .