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Hypercyclic behaviour of operators in a hypercyclic [formula omitted]-semigroup

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
244
Issue
1
Identifiers
DOI: 10.1016/j.jfa.2006.12.008
Keywords
  • Hypercyclic Vectors
  • [Formula Omitted]-Semigroups
  • Frequently Hypercyclic Operators
  • Chaotic Dynamics

Abstract

Abstract Let { T t } t ⩾ 0 be a hypercyclic strongly continuous semigroup of operators. Then each T t ( t > 0 ) is hypercyclic as a single operator, and it shares the set of hypercyclic vectors with the semigroup. This answers in the affirmative a natural question concerning hypercyclic C 0 -semigroups. The analogous result for frequent hypercyclicity is also obtained.

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