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Li–Yorke chaos for composition operators on \(L^p\)-spaces

  • N. C. BernardesJr.
  • U. B. DarjiEmail author
  • B. Pires
Article
  • 47 Downloads

Abstract

Li–Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful characterizations of this notion of chaos in the setting of linear dynamics were obtained recently. In this note we show that even simpler and more useful characterizations of Li–Yorke chaos can be given in the special setting of composition operators on \(L^p\)-spaces. As a consequence we obtain a simple characterization of weighted shifts which are Li–Yorke chaotic. We give numerous examples to show that our results are sharp.

Keywords

Li–Yorke chaos Composition operators \(L^p\)-spaces Weakly wandering sets 

Mathematics Subject Classification

Primary 47A16 47B33 Secondary 37D45 

Notes

Acknowledgements

The authors thank the referee whose valuable comments improved the presentation of the article.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada, Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  2. 2.Department of MathematicsUniversity of LouisvilleLouisvilleUSA
  3. 3.Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e LetrasUniversidade de São PauloRibeirão PretoBrazil

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