8 citations · 27 across the 9 of their papers we have counts for
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Weak limits of powers of Chacon's automorphism
Élise Janvresse, A. A. Prikhod'Ko, Thierry De La Rue +1
We completely describe the weak closure of the powers of the Koopman operator associated to Chacon's classical automorphism. We show that weak limits of these powers are the ortho-…
Ergodic automorphisms with simple spectrum characterized by fast correlation decay
A. A. Prikhod'ko
The existence of measure preserving invertible transformations with simple spectrum is established possessing the following rate of correlation decay $(f(T^k x), f(x)) = O(|k|^…
Lower bounds for symbolic complexity of iceberg dynamical systems
A. A. Prikhod'ko
The symbolic complexity of an infinite word is the function counting the number of different subwords in of length . In this paper our main purpose is to study…
On ergodic properties of iceberg transformations. I: Approximation and spectral multiplicity
A. A. Prikhod'ko
We investigate a class of mixing dynamical systems around the concept of iceberg transformation. In brief, an iceberg transformation is defined using symbolic language as follows.…
On flat trigonometric sums and ergodic flow with simple Lebesgue spectrum
A. A. Prikhod'ko
A complex polynomial is called unimodular if , . Littlewood asked the question (1966) on how close a unimodular polynomia…
A new class of Ornstein transformations with singular spectrum
El Houcein El Abdalaoui, François Parreau, A. A. Prikhod'Ko
It is shown that for any family of probability measures in Ornstein type constructions the corresponding transformation has almost surely a singular spectrum. This is a new general…