# American Institute of Mathematical Sciences

December  2009, 25(4): 1195-1208. doi: 10.3934/dcds.2009.25.1195

## Hypercyclic translation $C_0$-semigroups on complex sectors

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

Received  February 2009 Revised  June 2009 Published  September 2009

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.
Citation: José A. Conejero, Alfredo Peris. Hypercyclic translation $C_0$-semigroups on complex sectors. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1195-1208. doi: 10.3934/dcds.2009.25.1195
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