Ergodic -extensions over rational pure point spectrum, category and homomorphisms
Sur l'absence de mélange pour des flots spéciaux au-dessus d'une rotation irrationnelle
We prove the absence of mixing for special flows built over (1) an irrational rotation and under a function whose Fourier coefficients are of order O(1/|n|), and (2) an irrational rotation (satisfying a diophantine condition) and under a function having a finite number of singularities of a logarithmic type. These results generalize two theorems of Kochergin.
Cohomology groups, multipliers and factors in ergodic theory
The problem of compact factors in ergodic theory and its relationship with the problem of extending a cocycle to a cocycle of a larger action are studied.
On the rank of a class of bijective substitutions
Some new cases of realization of spectral multiplicity function for ergodic transformations
On symmetric logarithm and some old examples in smooth ergodic theory
We give a positive answer to the problem of existence of smooth weakly mixing but not mixing flows on some surfaces. More precisely, on each compact connected surface whose Euler characteristic is even and negative we construct smooth weakly mixing flows which are disjoint in the sense of Furstenberg from all mixing flows and from all Gaussian flows.
Ensemble d'invariants pour les produits croisés de Anzai
Extensions of Cocycles for Hyperfinite Actions and Applications.
Constructions of cocycles over irrational rotations
We construct a coboundary cocycle which is of bounded variation, is homotopic to the identity and is Hölder continuous with an arbitrary Hölder exponent smaller than 1.
Aproximation of Z-cocycles and shift dynamical systems.
Let Gbar = G{nt, nt | nt+1, t ≥ 0} be a subgroup of all roots of unity generated by exp(2πi/nt}, t ≥ 0, and let τ: (X, β, μ) O be an ergodic transformation with pure point spectrum Gbar. Given a cocycle φ, φ: X → Z2, admitting an approximation with speed 0(1/n1+ε, ε>0) there exists a Morse cocycle φ such that the corresponding transformations τφ and τ...
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].
On the multiplicity function of ergodic group extensions of rotations
For an arbitrary set A ⊆ ℕ satisfying 1 ∈ A and lcm(m₁,m₂) ∈ A whenever m₁,m₂ ∈ A, an ergodic abelian group extension of a rotation for which the range of the multiplicity function equals A is constructed.
Ergodic automorphisms whose weak closure of off-diagonal measures consists of ergodic self-joinings
Basic ergodic properties of the ELF class of automorphisms, i.e. of the class of ergodic automorphisms whose weak closure of measures supported on the graphs of iterates of T consists of ergodic self-joinings are investigated. Disjointness of the ELF class with: 2-fold simple automorphisms, interval exchange transformations given by a special type permutations and time-one maps of measurable flows is discussed. All ergodic Poisson suspension automorphisms as well as dynamical systems determined...
Quelques remarques sur les facteurs des systèmes dynamiques gaussiens
We study the factors of Gaussian dynamical systems which are generated by functions depending only on a finite number of coordinates. As an application, we show that for Gaussian automorphisms with simple spectrum, the partition is generating.
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