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Hypercyclic and chaotic semigroups of linear operators

Published online by Cambridge University Press:  02 April 2001

WOLFGANG DESCH,
WILHELM SCHAPPACHER and
GLENN F. WEBB
WOLFGANG DESCH
Affiliation:
Universität Graz, Institut für Mathematik, Heinrichstraße 36, A-8010 Graz, Austria
WILHELM SCHAPPACHER
Affiliation:
Universität Graz, Institut für Mathematik, Heinrichstraße 36, A-8010 Graz, Austria
GLENN F. WEBB
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
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Abstract

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We investigate hypercyclic and chaotic behavior of linear strongly continuoussemigroups. We give necessary and sufficient conditions on the semigroup tobehypercyclic, and sufficient conditions on the spectrum of an operator togenerate a hypercyclic semigroup. A variety of examples is provided.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 4 , August 1997, pp. 793 - 819
Copyright
© 1997 Cambridge University Press

Footnotes

Work by G. W. supported by the National Science Foundation under Grant No. DMS-9202550. Work by W. D. done within the Spezialforschungsbereich F 003,Optimierung und Kontrolle. Work by W. D. and W. S. supported in part by aSCIENCE project of the European Community.