On pairwise sensitivity

We define the concept of pairwise sensitivity with respect to initial conditions for the endomorphisms on Lebesgue metric spaces. The idea is that the orbits of almost every pair of nearby initial points (for the product of the invariant measure) of a pairwise sensitive map may diverge from a positive quantity independent of the initial points. We study the relationships between pairwise sensitivity and weak mixing, pairwise sensitivity and positiveness of metric entropy and we compute the largest sensitivity constant.  2005 Elsevier Inc. All rights reserved