Metric with ergodic geodesic flow is completely determined by unparameterized geodesics.
Matveev, Vladimir S., Topalov, Petar J. (2000)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Matveev, Vladimir S., Topalov, Petar J. (2000)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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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.
Keith Burns, Marlies Gerber (1994)
Journal für die reine und angewandte Mathematik
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D. J. Rudolph (1975)
Publications mathématiques et informatique de Rennes
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Yves Colin de Verdière (2012-2014)
Séminaire de théorie spectrale et géométrie
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In this paper, we present an extension of the classical Quantum ergodicity Theorem, due to Shnirelman, to the case of Laplacians with discontinous metrics along interfaces. The “geodesic flow” is then no more a flow, but a Markov process due to the fact that rays can by reflected or refracted at the interfaces. We give also an example build by gluing together two flat Euclidean disks.
Artur Avila, Marcelo Viana, Amie Wilkinson (2015)
Journal of the European Mathematical Society
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We consider volume-preserving perturbations of the time-one map of the geodesic flow of a compact surface with negative curvature. We show that if the Liouville measure has Lebesgue disintegration along the center foliation then the perturbation is itself the time-one map of a smooth volume-preserving flow, and that otherwise the disintegration is necessarily atomic.
Krzysztof Frączek, Mariusz Lemańczyk (2005)
Fundamenta Mathematicae
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Special flows over some locally rigid automorphisms and under L² ceiling functions satisfying a local L² Denjoy-Koksma type inequality are considered. Such flows are proved to be disjoint (in the sense of Furstenberg) from mixing flows and (under some stronger assumption) from weakly mixing flows for which the weak closure of the set of all instances consists of indecomposable Markov operators. As applications we prove that ∙ special flows built over ergodic interval...
S. G. Dani (1989)
Banach Center Publications
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William Parry (1974)
Compositio Mathematica
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Donald S. Ornstein (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.
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.
A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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A. O. Lopes, Ph. Thieullen (2006)
Annales de l'I.H.P. Analyse non linéaire
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