Beyond Lyapunov

Ergodic parameters like the Lyapunov and the conditional exponents are global functions of the invariant measure, but the invariant measure itself contains more information. A more complete characterization of the dynamics by new families of ergodic parameters is discussed, as well as their relation to the dynamical R'{e}nyi entropies and measures of self-organization. A generalization of the Pesin formula is derived which holds under some weak correlation conditions.