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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

We investigate hypercyclic and chaotic behavior of linear strongly continuous semigroups. We give necessary and sufficient conditions on the semigroup to be hypercyclic, and sufficient conditions on the spectrum of an operator to generate a hypercyclic semigroup. A variety of examples is provided.

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

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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 a SCIENCE project of the European Community.