Displaying similar documents to “Averaging method for differential equations perturbed by dynamical systems”

A property of ergodic 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.

On disjointness properties of some smooth flows

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...

Ratner's property for special flows over irrational rotations under functions of bounded variation. II

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,...