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Topologically transitive skew-products of operators

Published online by Cambridge University Press:  30 March 2009

FRÉDÉRIC BAYART ,
GEORGE COSTAKIS  and
DEMETRIS HADJILOUCAS
FRÉDÉRIC BAYART
Affiliation:
Université Blaise Pascal, Clermont-Ferrand, Laboratoire de Mathématiques, UMR 6620, Campus des Cézeaux, F-63177 Aubiere Cedex, France (email: bayart@math.univ-bpclermont.fr)
GEORGE COSTAKIS
Affiliation:
Department of Mathematics, University of Crete, Knossos Avenue, GR-714 09, Heraklion, Crete, Greece (email: costakis@math.uoc.gr)
DEMETRIS HADJILOUCAS
Affiliation:
The School of Sciences, European University Cyprus, 6 Diogenes Street, Engomi, PO Box 22006, 1516 Nicosia, Cyprus (email: d.hadjiloucas@euc.ac.cy)
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 1 , February 2010 , pp. 33 - 49
Copyright
Copyright © Cambridge University Press 2009

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