Integral Geometry of the action fof ST(3) on the space E...
Invariant Extensions of Positive Operators.
Invariant measures for actions of unipotent groups over local fields on homogeneous spaces.
Invariant measures for iterated function systems
A new criterion for the existence of an invariant distribution for Markov operators is presented. Moreover, it is also shown that the unique invariant distribution of an iterated function system is singular with respect to the Hausdorff measure.
Invariant measures for Markov operators with application to function systems
A new sufficient condition for the existence of an invariant measure for Markov operators defined on Polish spaces is presented. This criterion is applied to iterated function systems.
Invariant measures for nonexpansive Markov operators on Polish spaces [Book]
Les systèmes simples sont disjoints de ceux qui sont infiniment divisibles et plongeables dans un flot
We prove that simple transformations are disjoint from those which are infinitely divisible and embeddable in a flow. This is a reinforcement of a previous result of A. del Junco and M. Lemańczyk [1] who showed that simple transformations are disjoint from Gaussian processes.
Mixing automorphisms of compact groups and a theorem of Schlickewei.
Mixing for dyadic equivalence.
Mixing of all orders of Lie groups actions.
Mixing of all orders of Lie groups actions (Erratum).
Mixing properties of nearly maximal entropy measures for shifts of finite type
We prove that for a certain class of shifts of finite type with positive topological entropy there is always an invariant measure, with entropy arbitrarily close to the topological entropy, that has strong metric mixing properties. With the additional assumption that there are dense periodic orbits, one can ensure that this measure is Bernoulli.
Non singular transformations and spectral analysis of measures
Nonergodic actions, cocycles and superrigidity.
On continuous actions commutingwith actions of positive entropy
Let F and G be finitely generated groups of polynomial growth with the degrees of polynomial growth d(F) and d(G) respectively. Let be a continuous action of F on a compact metric space X with a positive topological entropy h(S). Then (i) there are no expansive continuous actions of G on X commuting with S if d(G)
On Ergodic Averages for Affine Lattice Actions on Tori.
On extremal and perfect σ-algebras for -actions on a Lebesgue space
We show that for every positive integer d there exists a -action and an extremal σ-algebra of it which is not perfect.
On group extensions of 2-fold simple ergodic actions
Compact group extensions of 2-fold simple actions of locally compact second countable amenable groups are considered. It is shown what the elements of the centralizer of such a system look like. It is also proved that each factor of such a system is determined by a compact subgroup in the centralizer of a normal factor.
On Invariant Measures, Minimal Sets and a Lemma of Margulies.
On regular generator of Z²-actions in exhaustive partitions