Displaying similar documents to “Weak mixing and product recurrence”

(Non-)weakly mixing operators and hypercyclicity sets

Frédéric Bayart, Étienne Matheron (2009)

Annales de l’institut Fourier

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We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space ℓ 1 ( ℕ ) , any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for c 0 ( ℕ ) or ℓ p ( ℕ ) , 1 < p < ∞ . Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.

Geometric realization and coincidence for reducible non-unimodular Pisot tiling spaces with an application to β -shifts

Veronica Baker, Marcy Barge, Jaroslaw Kwapisz (2006)

Annales de l’institut Fourier

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This article is devoted to the study of the translation flow on self-similar tilings associated with a substitution of Pisot type. We construct a geometric representation and give necessary and sufficient conditions for the flow to have pure discrete spectrum. As an application we demonstrate that, for certain beta-shifts, the natural extension is naturally isomorphic to a toral automorphism.

Weak mixing and eigenvalues for Arnoux-Rauzy sequences

Julien Cassaigne, Sébastien Ferenczi, Ali Messaoudi (2008)

Annales de l’institut Fourier

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We define by simple conditions two wide subclasses of the so-called Arnoux-Rauzy systems; the elements of the first one share the property of (measure-theoretic) weak mixing, thus we generalize and improve a counter-example to the conjecture that these systems are codings of rotations; those of the second one have eigenvalues, which was known hitherto only for a very small set of examples.

Infinite periodic points of endomorphisms over special confluent rewriting systems

Julien Cassaigne, Pedro V. Silva (2009)

Annales de l’institut Fourier

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We consider endomorphisms of a monoid defined by a special confluent rewriting system that admit a continuous extension to the completion given by reduced infinite words, and study from a dynamical viewpoint the nature of their infinite periodic points. For prefix-convergent endomorphisms and expanding endomorphisms, we determine the structure of the set of all infinite periodic points in terms of adherence values, bound the periods and show that all regular periodic points are attractors. ...

Convergence in Capacity

Yang Xing (2008)

Annales de l’institut Fourier

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We study the relationship between convergence in capacities of plurisubharmonic functions and the convergence of the corresponding complex Monge-Ampère measures. We find one type of convergence of complex Monge-Ampère measures which is essentially equivalent to convergence in the capacity C n of functions. We also prove that weak convergence of complex Monge-Ampère measures is equivalent to convergence in the capacity C n - 1 of functions in some case. As applications we give certain stability...