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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas

, Volume 105, Issue 2, pp 397-402

The set of periods of chaotic operators and semigroups

  • Gustavo A. Muñoz-FernándezAffiliated withDepartamento de Análisis Matemático, Universidad Complutense de Madrid
  • , Juan B. Seoane-SepúlvedaAffiliated withDepartamento de Análisis Matemático, Universidad Complutense de Madrid Email author 
  • , Andreas WeberAffiliated withInstitut für Algebra und Geometrie, KIT

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Abstract

This expository paper is devoted to the review of some very recent results concerning the set of periods of a chaotic operator T or a chaotic semigroup {T (t): t ≥  0} acting on a complex Banach space. We obtain information about the structure of the set of periods and we give techniques to construct (chaotic) strongly continuous semigroups with prescribed periods.

Keywords

Periods of strongly continuous semigroups Hypercyclic semigroups Chaotic semigroups

Mathematics Subject Classification (2000)

Primary 47A16 Secondary 47D06