Ergodic Automorphisms of Compact Metric Groups are Isomorphic to Bernoulli Shifts
Nobuo Aoki (1975)
Publications mathématiques et informatique de Rennes
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Nobuo Aoki (1975)
Publications mathématiques et informatique de Rennes
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Nobuo Aoki (1985)
Colloquium Mathematicae
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Y. Derriennic, K. Frączek, M. Lemańczyk, F. Parreau (2008)
Colloquium Mathematicae
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Basic ergodic properties of the ELF class of automorphisms, i.e. of the class of ergodic automorphisms whose weak closure of measures supported on the graphs of iterates of T consists of ergodic self-joinings are investigated. Disjointness of the ELF class with: 2-fold simple automorphisms, interval exchange transformations given by a special type permutations and time-one maps of measurable flows is discussed. All ergodic Poisson suspension automorphisms as well as dynamical systems...
Jan Kwiatkowski, Mariusz Lemańczyk (1989)
Banach Center Publications
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Mariusz Lemańczyk (1988)
Studia Mathematica
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R. Sato (1990)
Colloquium Mathematicae
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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.
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.
Raja, C.Robinson Edward (2009)
The New York Journal of Mathematics [electronic only]
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Brian Marcus (1980)
Monatshefte für Mathematik
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Janusz Woś (1987)
Colloquium Mathematicae
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L. Varecza (1976)
Matematički Vesnik
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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.
Lindenstrauss, Elon (1999)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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A. M. Vershik (1989)
Banach Center Publications
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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.