Ergodic Theory and Dynamical Systems



Hypercyclic and chaotic semigroups of linear operators


WOLFGANG DESCH a1, WILHELM SCHAPPACHER a1 and GLENN F. WEBB a2
a1 Universität Graz, Institut für Mathematik, Heinrichstraße 36, A-8010 Graz, Austria
a2 Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA

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.

(Received March 6 1995)
(Revised February 21 1996)



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.