Ergodic Automorphisms of Compact Groups
D. A. Lind (1975)
Publications mathématiques et informatique de Rennes
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D. A. Lind (1975)
Publications mathématiques et informatique de Rennes
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R. Sato (1990)
Colloquium Mathematicae
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Jan Kwiatkowski, Mariusz Lemańczyk (1989)
Banach Center Publications
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Lasha Ephremidze, Ryotaro Sato (2005)
Colloquium Mathematicae
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A weighted ergodic maximal equality is proved for a conservative and ergodic semiflow of nonsingular automorphisms.
Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Mariusz Lemańczyk (1988)
Studia Mathematica
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Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Geoffrey R. Goodson (2007)
Colloquium Mathematicae
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Let S and T be automorphisms of a standard Borel probability space. Some ergodic and spectral consequences of the equation ST = T²S are given for T ergodic and also when Tⁿ = I for some n>2. These ideas are used to construct examples of ergodic automorphisms S with oscillating maximal spectral multiplicity function. Other examples illustrating the theory are given, including Gaussian automorphisms having simple spectra and conjugate to their squares.
Janusz Woś (1987)
Colloquium Mathematicae
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Nobuo Aoki (1975)
Publications mathématiques et informatique de Rennes
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Roland Zweimüller (2004)
Colloquium Mathematicae
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We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.
Maria Joiţa, Radu-B. Munteanu (2014)
Studia Mathematica
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We introduce a property of ergodic flows, called Property B. We prove that an ergodic hyperfinite equivalence relation of type III₀ whose associated flow has this property is not of product type. A consequence is that a properly ergodic flow with Property B is not approximately transitive. We use Property B to construct a non-AT flow which-up to conjugacy-is built under a function with the dyadic odometer as base automorphism.
Burgess Davis (1982)
Studia Mathematica
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Goodson, G.R. (1999)
Acta Mathematica Universitatis Comenianae. New Series
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J. Woś (1987)
Colloquium Mathematicae
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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.
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.
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...