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