Topologically transitive skew-products of operators

The purpose of the present paper is to provide a link between skew-product systems and linear dynamics. In particular, we give a criterion for skew-products of linear operators to be topologically transitive. This is then applied to certain families of linear operators including scalar multiples of...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2010-02, Vol.30 (1), p.33-49
Main Authors: BAYART, FRÉDÉRIC, COSTAKIS, GEORGE, HADJILOUCAS, DEMETRIS
Format: Article
Language:English
Subjects:
Differential equations
Functional Analysis
Linear equations
Mathematics
Topological manifolds
Vector space
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Summary:The purpose of the present paper is to provide a link between skew-product systems and linear dynamics. In particular, we give a criterion for skew-products of linear operators to be topologically transitive. This is then applied to certain families of linear operators including scalar multiples of the backward shift, backward unilateral weighted shifts, composition, translation and differentiation operators. We also prove the existence of common hypercyclic vectors for certain families of skew-product systems.
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385708001065