Displaying similar documents to “Geometry and dynamics of admissible metrics in measure spaces”

An observation on the Turán-Nazarov inequality

Omer Friedland, Yosef Yomdin (2013)

Studia Mathematica

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The main observation of this note is that the Lebesgue measure μ in the Turán-Nazarov inequality for exponential polynomials can be replaced with a certain geometric invariant ω ≥ μ, which can be effectively estimated in terms of the metric entropy of a set, and may be nonzero for discrete and even finite sets. While the frequencies (the imaginary parts of the exponents) do not enter the original Turán-Nazarov inequality, they necessarily enter the definition of ω.

Metric Entropy of Nonautonomous Dynamical Systems

Christoph Kawan (2014)

Nonautonomous Dynamical Systems

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We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn, μn) of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1. This notion generalizes the classical concept of metric entropy established by Kolmogorov and Sinai, and is related via a variational inequality to the topological entropy of nonautonomous systems as defined by Kolyada, Misiurewicz, and Snoha. Moreover, it shares several properties with the...

Partition sensitivity for measurable maps

C. A. Morales (2013)

Mathematica Bohemica

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We study countable partitions for measurable maps on measure spaces such that, for every point x , the set of points with the same itinerary as that of x is negligible. We prove in nonatomic probability spaces that every strong generator (Parry, W., Aperiodic transformations and generators, J. London Math. Soc. 43 (1968), 191–194) satisfies this property (but not conversely). In addition, measurable maps carrying partitions with this property are aperiodic and their corresponding spaces...