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-Fernández
    • Departamento de Análisis MatemáticoUniversidad Complutense de Madrid
    • Departamento de Análisis MatemáticoUniversidad Complutense de Madrid
  • Andreas Weber
    • Institut für Algebra und Geometrie, KIT

DOI: 10.1007/s13398-011-0016-8

Cite this article as:
Muñoz-Fernández, G.A., Seoane-Sepúlveda, J.B. & Weber, A. RACSAM (2011) 105: 397. doi:10.1007/s13398-011-0016-8


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.


Periods of strongly continuous semigroupsHypercyclic semigroupsChaotic semigroups

Mathematics Subject Classification (2000)

Primary 47A16Secondary 47D06

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© Springer-Verlag 2011