Displaying similar documents to “Minimal generators for aperiodic endomorphisms”

Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation

Alejandro Passeggi, Martín Sambarino (2013)

Fundamenta Mathematicae

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We prove that for every ϵ > 0 there exists a minimal diffeomorphism f: ² → ² of class C 3 - ϵ and semiconjugate to an ergodic translation with the following properties: zero entropy, sensitivity to initial conditions, and Li-Yorke chaos. These examples are obtained through the holonomy of the unstable foliation of Mañé’s example of a derived-from-Anosov diffeomorphism on ³.

An anti-classification theorem for ergodic measure preserving transformations

Matthew Foreman, Benjamin Weiss (2004)

Journal of the European Mathematical Society

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Despite many notable advances the general problem of classifying ergodic measure preserving transformations (MPT) has remained wide open. We show that the action of the whole group of MPT’s on ergodic actions by conjugation is turbulent in the sense of G. Hjorth. The type of classifications ruled out by this property include countable algebraic objects such as those that occur in the Halmos–von Neumann theorem classifying ergodic MPT’s with pure point spectrum. We treat both the classical...

Ergodic theorems in fully symmetric spaces of τ-measurable operators

Vladimir Chilin, Semyon Litvinov (2015)

Studia Mathematica

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Junge and Xu (2007), employing the technique of noncommutative interpolation, established a maximal ergodic theorem in noncommutative L p -spaces, 1 < p < ∞, and derived corresponding maximal ergodic inequalities and individual ergodic theorems. In this article, we derive maximal ergodic inequalities in noncommutative L p -spaces directly from the results of Yeadon (1977) and apply them to prove corresponding individual and Besicovitch weighted ergodic theorems. Then we extend these...

Strongly mixing sequences of measure preserving transformations

Ehrhard Behrends, Jörg Schmeling (2001)

Czechoslovak Mathematical Journal

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We call a sequence ( T n ) of measure preserving transformations strongly mixing if P ( T n - 1 A ∩ B ) tends to P ( A ) P ( B ) for arbitrary measurable A , B . We investigate whether one can pass to a suitable subsequence ( T n k ) such that 1 K ∑ k = 1 K f ( T n k ) ⟶ ∫ f d P almost surely for all (or “many”) integrable f .