Chaotic sets of shift and weighted shift maps Original Research Article

In this paper Li–Yorke chaotic sets generated by shift and weighted shift maps are studied. The characterization of Li–Yorke chaotic sets by pp-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.