Displaying similar documents to “Rank and spectral multiplicity”

Aproximation of Z-cocycles and shift dynamical systems.

I. Filipowicz, J. Kwiatkowski, M. Lemanczyk (1988)

Publicacions Matemàtiques

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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...

On the multiplicity function of ergodic group extensions of rotations

G. Goodson, J. Kwiatkowski, M. Lemańczyk, P. Liardet (1992)

Studia Mathematica

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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.

Disjointness of the convolutionsfor Chacon's automorphism

A. Prikhod'ko, V. Ryzhikov (2000)

Colloquium Mathematicum

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The purpose of this paper is to show that if σ is the maximal spectral type of Chacon’s transformation, then for any d ≠ d’ we have σ * d ⊥ σ * d ' . First, we establish the disjointness of convolutions of the maximal spectral type for the class of dynamical systems that satisfy a certain algebraic condition. Then we show that Chacon’s automorphism belongs to this class.

Automorphisms with finite exact uniform rank

Mieczysław Mentzen (1991)

Studia Mathematica

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The notion of exact uniform rank, EUR, of an automorphism of a probability Lebesgue space is defined. It is shown that each ergodic automorphism with finite EUR is finite extension of some automorphism with rational discrete spectrum. Moreover, for automorphisms with finite EUR, the upper bounds of EUR of their factors and ergodic iterations are computed.