Relative generators for the action of a countable abelian group on a Lebesgue space
Relatively perfect σ-algebras for flows
We show that for every ergodic flow, given any factor σ-algebra ℱ, there exists a σ-algebra which is relatively perfect with respect to ℱ. Using this result and Ornstein's isomorphism theorem for flows, we give a functorial definition of the entropy of flows.
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.
Répartition de Suites et Équations Fonctionnelles Associées.
Répartition et ergodicité
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.
Representations of flows and generalized Rudolph's theorem [Abstract of thesis]
Résolution d'une équation fonctionnelle
Rigid reparametrizations and cohomology for horocycle flows.
Rigidity and cocycles for ergodic actions of semi-simple Lie groups
Rigidity of Furstenberg entropy for semisimple Lie group actions
Rigidity of some translations on homogeneous spaces.
Rigidity results for Bernoulli actions and their von Neumann algebras
Using very original methods from operator algebras, Sorin Popa has shown that the orbit structure of the Bernoulli action of a property (T) group, completely remembers the group and the action. This information is even essentially contained in the crossed product von Neumann algebra. This is the first von Neumann strong rigidity theorem in the literature. The same methods allow Popa to obtain II factors with prescribed countable fundamental group.
Rotations sur les groupes, nombres algébriques, et substitutions
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...