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

Pesin's identity provides a profound connection between the Kolmogorov-Sinai entropy hKS and the Lyapunov exponent λ. It is well known that many systems exhibit subexponential separation of nearby trajectories and then λ=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 δxt=δx0eλαtα with 0<α<1. The limit distribution of λα is the inverse Lévy function. The average λα 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.