Distributionally n-Scrambled Set for Weighted Shift Operators

Distributionally n-Scrambled Set for Weighted Shift Operators The aim of the present paper is to investigate distributionally n-scrambled sets for weighted shift operators. We prove that the unilateral weighted shift operator admits densely invariant distributionally n-ε-scrambled linear manifolds for any ε ∈ (0, 1) and any integer n ⩾ 2, showing that this operator can exhibit maximal distributional n-chaos on a dense invariant linear manifold. Analogous results for the bilateral weighted shift operator are also obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Dynamical and Control Systems Springer Journals

Distributionally n-Scrambled Set for Weighted Shift Operators

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Engineering; Vibration, Dynamical Systems, Control; Calculus of Variations and Optimal Control; Optimization; Analysis; Applications of Mathematics; Systems Theory, Control
ISSN
1079-2724
eISSN
1573-8698
D.O.I.
10.1007/s10883-017-9359-6
Publisher site
See Article on Publisher Site

Abstract

The aim of the present paper is to investigate distributionally n-scrambled sets for weighted shift operators. We prove that the unilateral weighted shift operator admits densely invariant distributionally n-ε-scrambled linear manifolds for any ε ∈ (0, 1) and any integer n ⩾ 2, showing that this operator can exhibit maximal distributional n-chaos on a dense invariant linear manifold. Analogous results for the bilateral weighted shift operator are also obtained.

Journal

Journal of Dynamical and Control SystemsSpringer Journals

Published: Jan 18, 2017

References

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