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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hyperbolic composition operators on the ball


Authors: F. Bayart and S. Charpentier
Journal: Trans. Amer. Math. Soc. 365 (2013), 911-938
MSC (2010): Primary 47B33; Secondary 32A35
Published electronically: August 9, 2012
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Abstract: We give a classification, up to automorphisms, of hyperbolic linear fractional maps of the ball. We then show that this classification is very convenient to study the geometric properties of these maps, as well as the spectrum and the dynamics of the associated composition operators. We conclude by showing how these properties can be transfered to composition operators associated to hyperbolic self-maps of the ball which are not linear-fractional maps.


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Additional Information

F. Bayart
Affiliation: Laboratoire de Mathématiques, Clermont Université, Université Blaise Pascal, BP 10448, F-63000 CLERMONT-FERRAND, CNRS, UMR 6620, Laboratoire de Mathéma- tiques, F-63177 Aubiere, France
Email: Frederic.Bayart@math.univ-bpclermont.fr

S. Charpentier
Affiliation: Laboratoire de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405 Orsay, France
Address at time of publication: Centre de Mathématiques et Informatique (CMI), Aix-Marseille Université, Technopôle Château-Gombert, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13, France
Email: stephane.charpentier@math.u-psud.fr, stecharp@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05646-7
PII: S 0002-9947(2012)05646-7
Keywords: Composition operators, hypercyclicity, linear fractional maps, supercyclicity
Received by editor(s): June 15, 2010
Received by editor(s) in revised form: June 10, 2011
Published electronically: August 9, 2012
Article copyright: © Copyright 2012 American Mathematical Society