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K. Frączek, M. Lemańczyk (2003)
Fundamenta Mathematicae
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We give a positive answer to the problem of existence of smooth weakly mixing but not mixing flows on some surfaces. More precisely, on each compact connected surface whose Euler characteristic is even and negative we construct smooth weakly mixing flows which are disjoint in the sense of Furstenberg from all mixing flows and from all Gaussian flows.
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.
S. G. Dani (1989)
Banach Center Publications
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Adam Kanigowski (2014)
Colloquium Mathematicae
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We consider special flows over the rotation on the circle by an irrational α under roof functions of bounded variation. The roof functions, in the Lebesgue decomposition, are assumed to have a continuous singular part coming from a quasi-similar Cantor set (including the devil's staircase case). Moreover, a finite number of discontinuities is allowed. Assuming that α has bounded partial quotients, we prove that all such flows are weakly mixing and enjoy the weak Ratner property. Moreover,...
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...
William Parry (1974)
Compositio Mathematica
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D. J. Rudolph (1975)
Publications mathématiques et informatique de Rennes
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Brian Marcus (1978)
Inventiones mathematicae
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Kochergin, A. (2004)
Electronic Research Announcements of the American Mathematical Society [electronic only]
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Miroslav Krutina (1989)
Commentationes Mathematicae Universitatis Carolinae
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Sarah Iams, Brian Katz, Cesar E. Silva, Brian Street, Kirsten Wickelgren (2005)
Colloquium Mathematicae
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We study weak mixing and double ergodicity for nonsingular actions of locally compact Polish abelian groups. We show that if T is a nonsingular action of G, then T is weakly mixing if and only if for all cocompact subgroups A of G the action of T restricted to A is weakly mixing. We show that a doubly ergodic nonsingular action is weakly mixing and construct an infinite measure-preserving flow that is weakly mixing but not doubly ergodic. We also construct an infinite measure-preserving...
Miroslav Krutina (1989)
Commentationes Mathematicae Universitatis Carolinae
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Françoise Pène (2010)
ESAIM: Probability and Statistics
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In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we...