Some Notes on Li-Yorke Theorem and Li-Yorke Chaos

Using some lemmas, we simplify the proof of Li-Yorke theorem, so the definition of Li-Yorke chaos is more concise. At the same time, we reduce the difficulty of seeking conditions of satisfying Li-Yorke chaos. Further, we give a sufficient condition that Li-Yorke´s scrambled set is made up of non-wandering points in transitive dynamical system. It complements Li-York theorem.