  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.
