Linear Chaos pp 161-178 | Cite as

Connectedness arguments in linear dynamics

Part of the Universitext book series (UTX)


This chapter presents some of the deepest, most beautiful and most useful results from linear dynamics. We obtain Ansari’s theorem that every power of a hypercyclic operator is hypercyclic, the Bourdon–Feldman theorem that every somewhere dense orbit is (everywhere) dense, the Costakis–Peris theorem that every multi-hypercyclic operator is hypercyclic, the León–Müller theorem that any unimodular multiple of a hypercyclic operator is hypercyclic, and the Conejero–Müller–Peris theorem that every operator in a hypercyclic semigroup is hypercyclic.


Banach Space Unit Circle Positive Answer Dense Range Linear Dynamic 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Karl-G. Grosse-Erdmann
    • 1
  • Alfred Peris Manguillot
    • 2
  1. 1.Institut de MathématiqueUniversité de MonsMonsBelgium
  2. 2.Institut Universitari de Matemàtica Pura i AplicadaUniversitat Politècnica de ValènciaValènciaSpain

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