Propriétés arithmétiques presque sures des convergents
Spectrum of multidimensional dynamical systems with positive entropy
Applying methods of harmonic analysis we give a simple proof of the multidimensional version of the Rokhlin-Sinaǐ theorem which states that a Kolmogorov -action on a Lebesgue space has a countable Lebesgue spectrum. At the same time we extend this theorem to -actions. Next, using its relative version, we extend to -actions some other general results connecting spectrum and entropy.
Additive functions with respect to expansions over the set of Gaussian integers
Ensemble d'invariants pour les produits croisés de Anzai
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 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.
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