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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Manuel Stadlbauer (2004)
Fundamenta Mathematicae
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For a non-compact hyperbolic surface M of finite area, we study a certain Poincaré section for the geodesic flow. The canonical, non-invertible factor of the first return map to this section is shown to be pointwise dual ergodic with return sequence (aₙ) given by aₙ = π/(4(Area(M) + 2π)) · n/(log n). We use this result to deduce that the section map itself is rationally ergodic, and that the geodesic flow associated to M is ergodic with respect to the...
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...
Carlo Pandiscia (2014)
Confluentes Mathematici
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Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.
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.
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.
J. Bolton (1979)
Mathematische Annalen
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Keith Burns, Marlies Gerber (1994)
Journal für die reine und angewandte Mathematik
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Jens Heber (1994)
Mathematische Zeitschrift
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W. Thirring (1992)
Recherche Coopérative sur Programme n°25
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S. G. Dani (1989)
Banach Center Publications
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Lim, Sin Liang, Sagar, B.S.Daya (2008)
Discrete Dynamics in Nature and Society
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Toshikazu Sunada (1983)
Compositio Mathematica
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Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat (2014-2015)
Séminaire Laurent Schwartz — EDP et applications
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This paper is a proceedings version of [6], in which we state a Quantum Ergodicity (QE) theorem on a 3D contact manifold, and in which we establish some properties of the Quantum Limits (QL). We consider a sub-Riemannian (sR) metric on a compact 3D manifold with an oriented contact distribution. There exists a privileged choice of the contact form, with an associated Reeb vector field and a canonical volume form that coincides with the Popp measure. We state a QE theorem...
C. Yue (1996)
Geometric and functional analysis
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J. González-Dávila, L. Vanhecke (1994)
Colloquium Mathematicae
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