Topologically transitive skew-products of operators

• Autores: Frédéric Bayart , George Costakis, D. Hadjiloucas
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 30, Nº 1, 2010, págs. 33-49
• Idioma: inglés
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• Resumen

  • 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 opologically 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.