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.
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Supported by NNSF of China (Grant Nos. 11371339, 11431012, 11401362, 11471125) and NSF of Guangdong province (Grant No. S2013040014084)
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Li, J., Ye, X.D. Recent development of chaos theory in topological dynamics. Acta. Math. Sin.-English Ser. 32, 83–114 (2016). https://doi.org/10.1007/s10114-015-4574-0
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DOI: https://doi.org/10.1007/s10114-015-4574-0
Keywords
- Li–Yorke chaos
- Devaney chaos
- sensitive dependence on initial conditions
- distributional chaos
- weak mixing
- topological entropy
- Furstenberg family