Porosity and hypercyclic operators

Bayart, Frédéric

doi:10.1090/S0002-9939-05-07842-1

Porosity and hypercyclic operators
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by Frédéric Bayart

Proc. Amer. Math. Soc. 133 (2005), 3309-3316

DOI: https://doi.org/10.1090/S0002-9939-05-07842-1

Published electronically: May 9, 2005

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Abstract:

We study if the set of hypercyclic vectors of a hypercyclic operator is the complement of a $\sigma$-porous set. This leads to interesting results for both points of view: a limitation of the size of hypercyclic vectors, and new examples of first category sets which are not $\sigma$-porous.

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