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1
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Factors of ergodic group extensions of rotations

100%
Kwiatkowski J.
Studia Mathematica
|
1992
|
tom 103
|
nr 2
123-131
EN
Diagonal metric subgroups of the metric centralizer $C(T_φ)$ of group extensions are investigated. Any diagonal compact subgroup Z of $C(T_φ)$ is determined by a compact subgroup Y of a given metric compact abelian group X, by a family ${v_y : y ∈ Y}$, of group automorphisms and by a measurable function f:X → G (G a metric compact abelian group). The group Z consists of the triples $(y,F_y,v_y)$, y ∈ Y, where $F_y(x) = v_y(f(x)) - f(x+y)$, x ∈ X.
2
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Inverse limit of M -cocycles and applications

100%
Kwiatkowski J.
Fundamenta Mathematicae
|
1998
|
tom 157
|
nr 2-3
261-276
EN
For any m, 2 ≤ m < ∞, we construct an ergodic dynamical system having spectral multiplicity m and infinite rank. Given r > 1, 0 < b < 1 such that rb > 1 we construct a dynamical system (X, B, μ, T) with simple spectrum such that r(T) = r, F*(T) = b, and $#C(T)/wcl{T^n: n ∈ ℤ} = ∞$
3
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Rank and spectral multiplicity

64%
Ferenczi S., Kwiatkowski J.
Studia Mathematica
|
1992
|
tom 102
|
nr 2
121-144
EN
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.
4
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Minimal self-joinings and positive topological entropy II

64%
Blanchard F., Kwiatkowski J.
Studia Mathematica
|
1998
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tom 128
|
nr 2
121-133
EN
An effective construction of positive-entropy almost one-to-one topological extensions of the Chacón flow is given. These extensions have the property of almost minimal power joinings. For each possible value of entropy there are uncountably many pairwise non-conjugate such extensions.
5
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Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers

64%
Bułatek W., Kwiatkowski J.
Studia Mathematica
|
1992
|
tom 103
|
nr 2
133-142
EN
A class of strictly ergodic Toeplitz flows with positive entropies and trivial topological centralizers is presented.
6
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The centralizer of ergodic theory group extensions

64%
Kwiatkowski J., Lemańczyk M.
Banach Center Publications
|
1989
|
tom 23
|
nr 1
455-463
7
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Spectral isomorphisms of Morse flows

51%
Downarowicz T., Kwiatkowski J., Lacroix Y.
Fundamenta Mathematicae
|
2000
|
tom 163
|
nr 3
193-213
EN
A combinatorial description of spectral isomorphisms between Morse flows is provided. We introduce the notion of a regular spectral isomorphism and we study some invariants of such isomorphisms. In the case of Morse cocycles taking values in $G = ℤ_p$, where p is a prime, each spectral isomorphism is regular. The same holds true for arbitrary finite abelian groups under an additional combinatorial condition of asymmetry in the defining Morse sequence, and for Morse flows of rank one. Rank one is shown to be a spectral invariant in the class of Morse flows.
8
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The centralizer of Morse shifts induced by arbitrary blocks

38%
Kwiatkowski J., Rojek T.
Studia Mathematica
|
1988
|
tom 88
|
nr 2
165-181
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