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Compositional hypercyclicity equals supercyclicity


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Opened Access Compositional hypercyclicity equals supercyclicity
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Author: Bernal González, Luis
Bonilla Ramírez, Antonio Lorenzo
Calderón Moreno, María del Carmen
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2007
Published in: Houston Journal of Mathematics, 33 (2), 581-591.
Document type: Article
Abstract: In this note it is proved that the sequence of composition operators generated by automorphisms of a simply connected domain strictly contained in the complex plane is hypercyclic –that is, possesses some dense orbit– if and only if it is supercyclic –i.e., possesses some dense projective orbit–. When the domain is the full complex plane, a result in this direction is also obtained. In addition, a number of statements about the corresponding cyclicity properties of single composition operators are either proved directly or extracted as a consequence
Cite: Bernal González, L., Bonilla Ramírez, A.L. y Calderón Moreno, M.d.C. (2007). Compositional hypercyclicity equals supercyclicity. Houston Journal of Mathematics, 33 (2), 581-591.
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