Chaotic sets of shift and weighted shift maps

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.