Abstract
In this paper Li–Yorke chaotic sets generated by shift and weighted shift maps are studied. The characterization of Li–Yorke chaotic sets by p -scrambled sets, maximal scrambled sets and orbit invariants are proved for the general shift maps. For weighted shift maps on infinite-dimensional spaces, the necessary and sufficient conditions for Li–Yorke chaotic are proved both in the abstract sequence setting and in the eigenfunction setting. Besides, a constructive proof is provided for the Devaney chaos of weighted shift maps on the Schwartz space.
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