# American Institute of Mathematical Sciences

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July  2008, 20(3): 577-587. doi: 10.3934/dcds.2008.20.577

## Hypercyclicity and chaoticity spaces of $C_0$ semigroups

 1 School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa 2 Wydział Matematyki Informatyki i Mechaniki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa

Received  March 2007 Revised  August 2007 Published  December 2007

In [10] the author provided a generalization of the classical Desch-Schappacher-Webb sufficient criterion which ensures hypercyclicity of linear semigroups. In this paper we simplify assumptions of [10], obtaining new criteria for hypercyclicity of a $C_0$ semigroup in a subspace (sub-hypercyclicity), and also for its sub-chaoticity. Moreover, we provide full characterization of chaoticity and hypercyclicity spaces of semigroups satisfying the assumptions of these new criteria. We also present examples showing that, in general, these assumptions cannot be weakened.
Citation: Jacek Banasiak, Marcin Moszyński. Hypercyclicity and chaoticity spaces of $C_0$ semigroups. Discrete & Continuous Dynamical Systems, 2008, 20 (3) : 577-587. doi: 10.3934/dcds.2008.20.577
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