Hypercyclic operators and rotated orbits with polynomial phases

An important result of León-Saavedra and M\"uller says that the rotations of hypercyclic operators remain hypercyclic. We provide extensions of this result for orbits of operators which are rotated by unimodular complex numbers with polynomial phases. On the other hand, we show that this fails...

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Bibliographic Details
Published in:arXiv.org 2013-03
Main Authors: Bayart, Frédéric, Costakis, George
Format: Article
Language:English
Subjects:
Complex numbers
Operators
Orbits
Phases
Polynomials
Online Access:Get full text
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Summary:An important result of León-Saavedra and M\"uller says that the rotations of hypercyclic operators remain hypercyclic. We provide extensions of this result for orbits of operators which are rotated by unimodular complex numbers with polynomial phases. On the other hand, we show that this fails for unimodular complex numbers whose phases grow to infinity too quickly, say at a geometric rate. A further consequence of our work is a notable strengthening of a result due to Shkarin which concerns variants of León-Saavedra and M\"uller's result in a non-linear setting.
ISSN:2331-8422
DOI:10.48550/arxiv.1304.0176