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 .
Singularité des produits de Anzai associés aux fonctions caractéristiques d'un intervalle
Skew products in the centralizer of compact abelian group extensions.
Slow entropy type invariants and smooth realization of commuting measure-preserving transformations
Smooth Extensions of Bernoulli Shifts
For homographic extensions of the one-sided Bernoulli shift we construct σ-finite invariant and ergodic product measures. We apply the above to the description of invariant product probability measures for smooth extensions of one-sided Bernoulli shifts.
Smooth Non-Bernoulli K-Automorphisms.
Sofic Systems and Graphs.
Solenoidal Automorphisms with Specifications.
Solvability of the functional equation f = (T-I)h for vector-valued functions
Let X be a reflexive Banach space and (Ω,,μ) be a probability measure space. Let T: M(μ;X) → M(μ;X) be a linear operator, where M(μ;X) is the space of all X-valued strongly measurable functions on (Ω,,μ). We assume that T is continuous in the sense that if (fₙ) is a sequence in M(μ;X) and in measure for some f ∈ M(μ;X), then also in measure. Then we consider the functional equation f = (T-I)h, where f ∈ M(μ;X) is given. We obtain several conditions for the existence of h ∈ M(μ;X) satisfying...
Some combinatorial problems on the measurability of functions with respect to invariant extensions of the Lebesgue measure
Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point
Some new cases of realization of spectral multiplicity function for ergodic transformations
Some New Examples of Gibbs Measures.
Some properties od step-punctions connected with extensions of measures
Some Remarks Concerning an Example of a Minimal, Non-Uniquely Ergodic Interval Exchange Transformation.