Fluctuations of dynamical scaling indices in nonlinear systems.

Due to fluctuations around the metric entropy of chaotic dynamical systems there exists a spectrum of invariant dynamical scaling indices, complementary to the range of invariant static scaling indices which have been discovered and apphed recently. The basic scaling behavior in both cases is shown to be rooted in the thermodynamic formalism of dynamical systems. An explicit simple example of these ideas is given, stressing their use in characterizing complex behavior.