Recent development of chaos theory in topological dynamics
Jian Li, Xiangdong Ye
TL;DR
This paper reviews recent advances in chaos theory within topological dynamics, covering various types of chaos, entropy, and mixing properties, and explores their interrelations.
Contribution
It provides a comprehensive summary of recent developments and connections among different chaos concepts in topological dynamics.
Findings
Li-Yorke chaos, Devaney chaos, and distributional chaos are interconnected.
Positive topological entropy correlates with complex chaotic behavior.
Weakly mixing sets are significant in understanding chaos structures.
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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