Spectral properties of G-symbolic Morse shifts

Jan Kwiatkowski; Andrzej Sikorski

Displaying similar documents to “Spectral properties of G-symbolic Morse shifts”

Rank and spectral multiplicity

Sébastien Ferenczi, Jan Kwiatkowski (1992)

Studia Mathematica

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For a dynamical system (X,T,μ), we investigate the connections between a metric invariant, the rank r(T), and a spectral invariant, the maximal multiplicity m(T). We build examples of systems for which the pair (m(T),r(T)) takes values (m,m) for any integer m ≥ 1 or (p-1, p) for any prime number p ≥ 3.

The centralizer of Morse shifts

Mariusz Lemanczyk (1985)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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On the rank of a class of bijective substitutions

G. Goodson, M. Lemańczyk (1990)

Studia Mathematica

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Isomorphism of regular Morse dynamical systems induced by arbitrary blocks

J. Kwiatkowski (1986)

Studia Mathematica

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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.

Ergodic $Z_{2}$ -extensions over rational pure point spectrum, category and homomorphisms

M. Lemańczyk (1987)

Compositio Mathematica

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Some new cases of realization of spectral multiplicity function for ergodic transformations

A. Katok, M. Lemańczyk (2009)

Fundamenta Mathematicae

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Aproximation of Z-cocycles and shift dynamical systems.

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

Publicacions Matemàtiques

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Let Gbar = G{n_t, n_t | n_t+1, t ≥ 0} be a subgroup of all roots of unity generated by exp(2πi/n_t}, 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/n^1+ε, ε>0) there exists a Morse cocycle φ such that the corresponding transformations τ_φ...

Disjointness of the convolutionsfor Chacon's automorphism

A. Prikhod&#039;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.