Towards a Scaling Theory of Finite-Time Properties in Dynamical Systems?

It is suggested, on the basis of numerical simulations, that the (averaged) Lyapunov exponent at finite time of certain dynamical systems obeys universal scaling properties very similar to the scaling behaviour of the conductance in localization theory. An analytical approximation of the scaling function is derived from simple arguments. The possible mechanisms at the origin of this property are discussed, and the scaling function is proposed to be an important characterization of such dynamical systems.