A simple characterization of chaos for weighted composition $C_0$-semigroups on Lebesgue and Sobolev spaces

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A Simple Characterization of Chaos for Weighted Composition C0-semigroups on Lebesgue and Sobolev Spaces

The purpose of this article is to give a simple characterization of chaos for certain weighted composition C0-semigroups on Lebesgue spaces and Sobolev spaces over open intervals. Recall that a C0-semigroup T on a separable Banach space X is called chaotic if T is hypercyclic, i.e. there is x ∈ X such that {T (t)x; t ≥ 0} is dense in X , and if the set of periodic points, i.e. {x ∈ X ; ∃t > 0 :...

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ژورنال

عنوان ژورنال: Proceedings of the American Mathematical Society

سال: 2015

ISSN: 0002-9939,1088-6826

DOI: 10.1090/proc/12794