Some Open Problems in Ergodic Theory
Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Janusz Woś (1987)
Colloquium Mathematicae
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Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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R. Sato (1990)
Colloquium Mathematicae
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S. Doplicher, D. Kastler (1968)
Recherche Coopérative sur Programme n°25
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Burgess Davis (1982)
Studia Mathematica
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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.
Paweł Głowacki (1981)
Studia Mathematica
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J. Woś (1987)
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.
Teresa Bermúdez, Manuel González, Mostafa Mbekhta (1998)
Extracta Mathematicae
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Charles Pugh, Michael Shub (2000)
Journal of the European Mathematical Society
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In this paper we dramatically expand the domain of known stably ergodic, partially hyperbolic dynamical systems. For example, all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property are stably ergodic. Our main tools are the new concepts – julienne density point and julienne quasi-conformality of the stable and unstable holonomy maps. Julienne quasi-conformal holonomy maps preserve all julienne density points.
Karl Petersen, Shizuo Kakutani (1981)
Monatshefte für Mathematik
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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.
D. J. Rudolph (1975)
Publications mathématiques et informatique de Rennes
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Yves Derriennic (2010)
Colloquium Mathematicae
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The aim of this short note is to present in terse style the meaning and consequences of the "filling scheme" approach for a probability measure preserving transformation. A cohomological equation encapsulates the argument. We complete and simplify Woś' study (1986) of the reversibility of the ergodic limits when integrability is not assumed. We give short and unified proofs of well known results about the behaviour of ergodic averages, like Kesten's lemma (1975). The strikingly simple...
Jon Aaronson (1977)
Publications mathématiques et informatique de Rennes
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