Abstract

We introduce and study a concept which links the Li-Yorke versions of chaos with the notion of sensitivity to initial conditions. We call the system Li--Yorke sensitive if there exists $\epsilon >0$ such that every $x\; in\; X$ is a limit of points $x\; in\; X$ such that the pair $(x,y)$ is proximal but whose orbits are frequently at least $\epsilon$ apart. In particular, we show that this concept is strictly stronger than sensitivity and each weakly mixing systems are Li-Yorke sensitive. We also prove a generalization of results by Keynes, Robertson and Furstenberg concerning proximal cells of weakly mixing systems.