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Factors of ergodic group extensions of rotations

Jan Kwiatkowski — 1992

Studia Mathematica

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.

Inverse limit of M -cocycles and applications

Jan Kwiatkowski — 1998

Fundamenta Mathematicae

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 ) / w c l T n : n =

Rank and spectral multiplicity

Sébastien FerencziJan Kwiatkowski — 1992

Studia Mathematica

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.

Spectral isomorphisms of Morse flows

T. DownarowiczJan KwiatkowskiY. Lacroix — 2000

Fundamenta Mathematicae

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 = 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...

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