  We give a definition of generalized indicators of sensitivity to initial
conditions and orbit complexity (a measure of the information that is necessary
to describe the orbit of a given point).
  The well known Ruelle-Pesin and Brin-Katok theorems, combined with Brudno's
theorem give a relation between initial data sensitivity and orbit complexity
that is generalized in the present work.
  The generalized relation implies that the set of points where the sensitivity
to initial conditions is more than exponential in all directions is a 0
dimensional set. The generalized relation is then applied to the study of an
important example of weakly chaotic dynamics: the Manneville map.
