Pesin-type identity for intermittent dynamics with a zero Lyaponov exponent.

Pesin's identity provides a profound connection between the Kolmogorov-Sinai entropy h_{KS} and the Lyapunov exponent lambda. It is well known that many systems exhibit subexponential separation of nearby trajectories and then lambda=0. In many cases such systems are nonergodic and do not obey usual statistical mechanics. Here we investigate the nonergodic phase of the Pomeau-Manneville map where separation of nearby trajectories follows deltax_{t}=deltax_{0}e;{lambda_{alpha}t;{alpha}} with 0<alpha<1. The limit distribution of lambda_{alpha} is the inverse Lévy function. The average lambda_{alpha} is related to the infinite invariant density, and most importantly to entropy. Our work gives a generalized Pesin's identity valid for systems with an infinite invariant density.