Arithmetic Progressions and Chaos in Linear Dynamics

We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. We also show that this characterization does not hold for arbitrary Banach spaces. To achieve this, we study F -hypercyclicity for a family of su...

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Bibliographic Details
Published in:Integral equations and operator theory 2022-06, Vol.94 (2), Article 11
Main Authors: Cardeccia, Rodrigo, Muro, Santiago
Format: Article
Language:English
Subjects:
Analysis
Arithmetic
Banach spaces
Linear operators
Mathematics
Mathematics and Statistics
Number theory
Numbers
Progressions
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Summary:We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. We also show that this characterization does not hold for arbitrary Banach spaces. To achieve this, we study F -hypercyclicity for a family of subsets of the natural numbers associated to the existence of arbitrarily long arithmetic progressions.
ISSN:0378-620X
1420-8989
DOI:10.1007/s00020-022-02687-3