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A dynamical version of the Kuratowski–Mycielski theorem and invariant chaotic sets

Published online by Cambridge University Press:  24 January 2018

JIAN LI Open the ORCID record for JIAN LI [Opens in a new window] ,
JIE LÜ  and
YUANFEN XIAO
JIAN LI
Affiliation:
Department of Mathematics, Shantou University, Shantou, 515063, Guangdong, China email [email protected]
JIE LÜ
Affiliation:
School of Mathematics, South China Normal University, Guangzhou 510631, China email [email protected], [email protected]
YUANFEN XIAO
Affiliation:
School of Mathematics, South China Normal University, Guangzhou 510631, China email [email protected], [email protected]
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Abstract

We establish a dynamical version of the Kuratowski–Mycielski theorem on the existence of ‘large’ invariant dependent sets. We apply this result to the study of invariant chaotic sets in topological dynamical systems, simplify many known results on this topic and also obtain some new results.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 11 , November 2019 , pp. 3089 - 3110
Copyright
© Cambridge University Press, 2018 

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