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Li–Yorke chaos in linear dynamics

Published online by Cambridge University Press:  10 July 2014

N. C. BERNARDES JR ,
A. BONILLA ,
V. MÜLLER  and
A. PERIS
N. C. BERNARDES JR
Affiliation:
Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro, RJ 21945-970, Brazil email bernardes@im.ufrj.br
A. BONILLA
Affiliation:
Departamento de Análisis Matemático, Universidad de la Laguna, 38271, La Laguna (Tenerife), Spain email abonilla@ull.es
V. MÜLLER
Affiliation:
Mathematical Institute, Czech Academy of Sciences, Zitná 25, 115 67 Prague 1, Czech Republic email muller@math.cas.cz
A. PERIS
Affiliation:
IUMPA, Universitat Polit\`ecnica de Val\`encia, Departament de Matemàtica Aplicada, Edifici 7A, 46022 Val\`encia, Spain email aperis@mat.upv.es
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Abstract

We obtain new characterizations of Li–Yorke chaos for linear operators on Banach and Fréchet spaces. We also offer conditions under which an operator admits a dense set or linear manifold of irregular vectors. Some of our general results are applied to composition operators and adjoint multipliers on spaces of holomorphic functions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 6 , September 2015 , pp. 1723 - 1745
Copyright
© Cambridge University Press, 2014 

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