Random dynamics and its applications.
Random ergodic theorems for sub-Markovian operators
Random ergodic theorems with universally representative sequences
Range of density measures
We investigate some properties of density measures – finitely additive measures on the set of natural numbers extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the sequence as well as cluster points of some other similar sequences. We obtain range of possible values of density measures for any subset of . Our description of this range simplifies the description of Bhashkara Rao and Bhashkara Rao [Bhaskara Rao, K. P. S., Bhaskara Rao,...
Rank and spectral multiplicity
For a dynamical system (X,T,μ), we investigate the connections between a metric invariant, the rank r(T), and a spectral invariant, the maximal multiplicity m(T). We build examples of systems for which the pair (m(T),r(T)) takes values (m,m) for any integer m ≥ 1 or (p-1, p) for any prime number p ≥ 3.
Rank is not a spectral invariant
Rank-one group actions with simple mixing -subactions.
Rate of convergence of conditional entropies for some maps of an interval
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