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Bau-Sen Du introduced a notion of chaos which is stronger than Li-Yorke sensitivity. A TDS (X, f ) is called chaotic if there is a positive such that for any x and any nonempty open set V of X there is a point y in V such that the pair (x, y) is proximal but not -asymptotic. In this article, we show that a TDS (T, f ) is transitive but not mixing if and only if (T, f ) is Li-Yorke sensitive but not chaotic, where T is a tree. Moreover, we compare such chaos with other notions of chaos.
Akin et al. (Fri,) studied this question.