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Acta Mathematica Sinica, English Series

, Volume 32, Issue 1, pp 83–114 | Cite as

Recent development of chaos theory in topological dynamics

  • Jian LiEmail author
  • Xiang Dong Ye
Article

Abstract

We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li–Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.

Keywords

Li–Yorke chaos Devaney chaos sensitive dependence on initial conditions distributional chaos weak mixing topological entropy Furstenberg family 

MR(2010) Subject Classification

54H20 37B05 37B40 

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© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsShantou UniversityShantouP. R. China
  2. 2.Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences and School of MathematicsUniversity of Science and Technology of ChinaHefeiP. R. China

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