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Factors of ergodic group extensions of rotations

100%

Kwiatkowski J.

Studia Mathematica

1992

tom 103

nr 2

123-131

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.

A non-regular Toeplitz flow with preset pure point spectrum

51%

Downarowicz T., Lacroix Y.

Studia Mathematica

1996

tom 120

nr 3

235-246

Given an arbitrary countable subgroup $σ_0$ of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to $σ_0$. For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.

Toeplitz flows with pure point spectrum

51%

Iwanik A.

Studia Mathematica

1996

tom 118

nr 1

27-35

We construct strictly ergodic 0-1 Toeplitz flows with pure point spectrum and irrational eigenvalues. It is also shown that the property of being regular is not a measure-theoretic invariant for strictly ergodic Toeplitz flows.

Ograniczanie wyników

3 Studia Mathematica

1 Downarowicz T.

1 Iwanik A.

1 Kwiatkowski J.

1 Lacroix Y.

2 1996

1 1992

Wyniki wyszukiwania

Factors of ergodic group extensions of rotations

A non-regular Toeplitz flow with preset pure point spectrum

Toeplitz flows with pure point spectrum