Displaying similar documents to “Dense orbits of horospherical flows”

A property of ergodic flows

Maria Joiţa, Radu-B. Munteanu (2014)

Studia Mathematica

Similarity:

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

Similarity:

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...

Ergodic theory approach to chaos: Remarks and computational aspects

Paweł J. Mitkowski, Wojciech Mitkowski (2012)

International Journal of Applied Mathematics and Computer Science

Similarity:

We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor...

On subrelations of ergodic measured type III equivalence relations

Alexandre Danilenko (2000)

Colloquium Mathematicae

Similarity:

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.