Ergodic -extensions over rational pure point spectrum, category and homomorphisms
M. Lemańczyk (1987)
Compositio Mathematica
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M. Lemańczyk (1987)
Compositio Mathematica
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Jan Kwiatkowski, Mariusz Lemańczyk (1989)
Banach Center Publications
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Alexandre Danilenko, Mariusz Lemańczyk (1999)
Studia Mathematica
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We establish existence and uniqueness of a canonical form for isometric extensions of an ergodic non-singular transformation T. This is applied to describe the structure of commutors of the isometric extensions. Moreover, for a compact group G, we construct a G-valued T-cocycle α which generates the ergodic skew product extension and admits a prescribed subgroup in the centralizer of .
Tim Austin (2010)
Fundamenta Mathematicae
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We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such extensions rests on a simple notion of 'direct integral' for a 'measurable family' of homogeneous spaces, which has a number of precedents in older literature. The main contribution of the present paper is the systematic development of a formalism for handling...
Mahesh Nerurkar (2000)
Colloquium Mathematicae
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We construct continuous G-valued cocycles that are not cohomologous to any compact constant via a measurable transfer function, provided the underlying dynamical system is rigid and the range group G satisfies a certain general condition. For more general ergodic aperiodic systems, we also show that the set of continuous ergodic cocycles is residual in the class of all continuous cocycles provided the range group G is a compact connected Lie group. The first construction is based on...
Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Geoffrey Goodson (2000)
Colloquium Mathematicae
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We study certain symmetries that arise when automorphisms S and T defined on a Lebesgue probability space (X, ℱ, μ) satisfy the equation . In an earlier paper [6] it was shown that this puts certain constraints on the spectrum of T. Here we show that it also forces constraints on the spectrum of . In particular, has to have a multiplicity function which only takes even values on the orthogonal complement of the subspace . For S and T ergodic satisfying this equation further constraints...
Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Paweł Głowacki (1981)
Studia Mathematica
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A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Alexandre Danilenko (2000)
Colloquium Mathematicae
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We discuss the classification up to orbit equivalence of inclusions 𝑆 ⊂ ℛ of measured ergodic discrete hyperfinite equivalence relations. In the case of type III relations, the orbit equivalence classes of such inclusions of finite index are completely classified in terms of triplets consisting of a transitive permutation group G on a finite set (whose cardinality is the index of 𝑆 ⊂ ℛ), an ergodic nonsingular ℝ-flow V and a homomorphism of G to the centralizer of V.
Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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Teresa Bermúdez, Manuel González, Mostafa Mbekhta (2000)
Studia Mathematica
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We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.