Hypercyclic translation $C_0$-semigroups on  complex sectors

José A. Conejero; Alfredo Peris

doi:10.3934/dcds.2009.25.1195

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2009, Volume 25, Issue 4: 1195-1208. Doi: 10.3934/dcds.2009.25.1195

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Hypercyclic translation $C_0$-semigroups on complex sectors

José A. Conejero^1, and
Alfredo Peris^2,

1.
Instituto Universitario de Matemática Pura y Aplicada. Edificio 1H, Universidad Politécnica de Valencia, E-46022, Valencia
2.
Departament de Matemàtica Aplicada & IUMPA Edifici 7A, Universitat Politècnica de València, E-46022, València

Received: February 2009

Revised: June 2009

Published: November 2009

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Abstract

We study the hypercyclic behaviour of sequences of operators in a $C_0$-semigroup whose index set is a sector in the complex plane. The hypercyclicity and chaos for the concrete case of the translation semigroup is analyzed. Some examples are provided to complete the results.

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Mathematics Subject Classification: Primary: 47A16; Secondary: 47D06.

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