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Hypercyclic composition operators on spaces of real analytic functions†

Published online by Cambridge University Press:  07 June 2012

JOSÉ BONET  and
PAWEŁ DOMAŃSKI
JOSÉ BONET
Affiliation:
Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, E-46071 Valencia, Spain. e-mail: [email protected]
PAWEŁ DOMAŃSKI
Affiliation:
Faculty of Mathematics and Comp. Sci., A. Mickiewicz University Poznań, Umultowska 87, 61-614 Poznań, Poland. e-mail: [email protected]
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Abstract

We study the dynamical behaviour of composition operators Cϕ defined on spaces (Ω) of real analytic functions on an open subset Ω of ℝd. We characterize when such operators are topologically transitive, i.e. when for every pair of non-empty open sets there is an orbit intersecting both of them. Moreover, under mild assumptions on the composition operator, we investigate when it is sequentially hypercyclic, i.e., when it has a sequentially dense orbit. If ϕ is a self map on a simply connected complex neighbourhood U of ℝ, U ≠ ℂ, then topological transitivity, hypercyclicity and sequential hypercyclicity of Cϕ:(ℝ) → (ℝ) are equivalent.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 153 , Issue 3 , November 2012 , pp. 489 - 503
Copyright
Copyright © Cambridge Philosophical Society 2012

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Footnotes

†

Partially supported by MEC and FEDER Project MTM2010-15200.

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