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December 2012 Dense chaos and densely chaotic operators
Xinxing Wu, Peiyong Zhu
Tsukuba J. Math. 36(2): 367-375 (December 2012). DOI: 10.21099/tkbjm/1358777004

Abstract

The aim of this paper is to study dense chaos and densely chaotic operators on Banach spaces. First, we prove that a dynamical system is densely δ-chaotic for some δ > 0 if and only if it is densely chaotic and sensitive. Meanwhile, we also show that for general dynamical systems, Devaney chaos and dense chaos do not imply each other. Then, by using these results, we have that for a operator defined on a Banach space, dense chaos, dense δ-chaos, generic chaos and generic δ-chaos are equivalent and they are all strictly stronger than Li-Yorke chaos.

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Xinxing Wu. Peiyong Zhu. "Dense chaos and densely chaotic operators." Tsukuba J. Math. 36 (2) 367 - 375, December 2012. https://doi.org/10.21099/tkbjm/1358777004

Information

Published: December 2012
First available in Project Euclid: 21 January 2013

zbMATH: 1260.54055
MathSciNet: MR3058244
Digital Object Identifier: 10.21099/tkbjm/1358777004

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Rights: Copyright © 2013 University of Tsukuba, Institute of Mathematics

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Vol.36 • No. 2 • December 2012
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