Geodesic
Hypercyclic semigroups and somewhere dense orbits
[Semigroupes hypercycliques et orbites quelque part denses]
Costakis, George1 ; Peris, Alfredo2
1 Department of Mathematics, University of Maryland, College Park, MA 20742, USA
2 Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, 46071 Valencia, Spain
Comptes Rendus. Mathématique, Tome 335 (2002) no. 11, pp. 895-898

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We study hypercyclicity of linear strongly continuous semigroups. In the case of iterations of a single operator Bourdon and Feldman have recently proved that the existence of somewhere dense orbits implies hypercyclicity. We show the corresponding result for semigroups. As a consequence, a conjecture of Herrero concerning iterations of a single operator also holds for strongly continuous semigroups.

Nous étudions l'hypercyclicité des semigroupes linéaires et fortement continus. En ce qui concerne l'iteration d'un opérateur, Bourdon et Feldman ont montré que l'existence des orbites quelque part denses implique hypercyclicité. Nous démontrons le resultat correspondant pour des semigroupes. Une conséquence est la generalisation d'une conjecture de Herrero à des semigroupes.

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DOI : 10.1016/S1631-073X(02)02572-4

Costakis, George 1 ; Peris, Alfredo 2

1 Department of Mathematics, University of Maryland, College Park, MA 20742, USA
2 Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, 46071 Valencia, Spain 
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     title = {Hypercyclic semigroups and somewhere dense orbits},
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Costakis, George; Peris, Alfredo. Hypercyclic semigroups and somewhere dense orbits. Comptes Rendus. Mathématique, Tome 335 (2002) no. 11, pp. 895-898. doi: 10.1016/S1631-073X(02)02572-4

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