Minimal generators for aperiodic endomorphisms

Zbigniew S. Kowalski

Displaying similar documents to “Minimal generators for aperiodic endomorphisms”

Minimal generators for ergodic endomorphisms

Zbigniew Kowalski (1988)

Studia Mathematica

Similarity:

Examples of minimal diffeomorphisms on 𝕋² semiconjugate to an ergodic translation

Alejandro Passeggi, Martín Sambarino (2013)

Fundamenta Mathematicae

Similarity:

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

Similarity:

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

Similarity:

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

Similarity:

We call a sequence $(T_{n})$ of measure preserving transformations strongly mixing if $P (T_{n}^{- 1} A \cap B)$ 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 $\frac{1}{K} \sum_{k = 1}^{K} f (T_{n_{k}}) ⟶ \int f d P$ almost surely for all (or “many”) integrable $f$ .

Strictly ergodic, uniform positive entropy models

Eli Glasner, Benjamin Weiss (1994)

Bulletin de la Société Mathématique de France

Similarity:

Strictly ergodic patterns and entropy for interval maps.

Bobok, J. (2003)

Acta Mathematica Universitatis Comenianae. New Series

Similarity:

On the sequence of integer parts of a good sequence for the ergodic theorem

Emmanuel Lesigne (1995)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

If $(u_{n})$ is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts $([u_{n}])$ good for the ergodic theorem ? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem.

Residuality of dynamical morphisms

R. Burton, M. Keane, Jacek Serafin (2000)

Colloquium Mathematicae

Similarity:

We present a unified approach to the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein. We show that in a suitable space of measures those measures which define isomorphisms or respectively homomorphisms form residual subsets.