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DOI: 10.23952/jnfa.2025.20
Received October 5, 2024; Accepted February 17, 2025; Published June 25, 2025
Abstract. It is an open problem whether a homeomorphism on a compact metric space satisfying that each proper pair is either positively or negatively Li-Yorke, called completely Li-Yorke chaotic, can have positive entropy. In this paper, an affirmative answer to this question is given. Indeed, for each homeomorphism T with positive entropy such that each proper pair is not two-sided asymptotic, a completely Li-Yorke chaotic homeomorphism with positive entropy associated with the given homeomorphism can be constructed.
How to Cite this Article:
Z. Lin, X. Ye, Completely Li-Yorke chaotic homeomorphisms with positive entropy, J. Nonlinear Funct. Anal. 2025 (2025) 20.