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Hypercyclic and chaotic semigroups of linear operators. (English) Zbl 0910.47033

Summary: 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.

MSC:

47D06 One-parameter semigroups and linear evolution equations
47D03 Groups and semigroups of linear operators
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