Li-Yorke sensitivity

We introduce and study a concept which links the Li-Yorke versions of chaos with the notion of sensitivity to initial conditions. We say that a dynamical system (X, T) is Li-Yorke sensitive if there exists a positive epsilon such that every x is an element of X is a limit of points y is an element of X such that the pair (x, y) is proximal but not epsilon-asymptotic, i.e. for infinitely many positive integers i the distance rho (T-i(x), T-i(y)) is greater than epsilon but for any positive delta this distance is less than delta for infinitely many i.