Lyapunov Partition Functions for the Dimensions of Chaotic Sets

Multifractal dimension spectra for the stable and unstable manifolds of invariant chaotic sets are studied for the case of invertible two-dimensional maps. A dynamical partition-function formalism giving these dimensions in terms of local Lyapunov numbers is obtained. The relationship of the Lyapunov partition functions for stable and unstable manifolds to previous work is discussed.