The set of periods of chaotic operators and semigroups
type: Item
instance of: scholarly article
title: The set of periods of chaotic operators and semigroups
zbMATH Open document ID: 1268.47009
author: G. A. Muñoz-Fernández
author: J. B. Seoane-Sepúlveda
author: A. Weber
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2012-12-05T00:00:00Z
review text: This expository paper reviews recent, still unpublished results about the set of possible periods of a chaotic operator \(T\) or a chaotic semigroup \((T(t) : t \geq 0)\) of operators acting on an infinite dimensional complex Banach space \(X\). The results about a single operator are due to Conejero, Martínez-Giménez and Peris and those about semigroups to the authors of the article under review (cf. [Bull. Lond. Math. Soc. 44, No.~3, 480--488 (2012; Zbl 1251.47009)]). In the case of one single operator, the picture is rather complete: An infinite subset \(P\) of the natural numbers is the set of periods of a chaotic operator on a Banach (even a Hilbert) space if and only if \(P\) is closed under least common multiple. The similar question for semigroups seems to be more delicate and only partial results are obtained. The paper concludes with a list of open questions.
reviewed by: José Bonet
Mathematics Subject Classification ID: 47A16
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 6112717
zbMATH Keywords: periods of strongly continuous semigroups
zbMATH Keywords: hypercyclic semigroups
zbMATH Keywords: chaotic semigroups
MaRDI profile type: Publication
full work available at URL: s13398-011-0016-8
OpenAlex ID: W2018362345
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DOI: 10.1007/S13398-011-0016-8
description: scientific article; zbMATH DE number 6112717