The ƒ(a) formalism applied to the crossover from conservative to dissipative scaling behaviour in period doubling systems

We use the ƒ(a) (spectral dimension) formalism to give a global description of the crossover from conservative to dissipative scaling behaviour in period doubling systems. As a generic model we consider the two-dimensional Hénon map, for which the jacobian 0 ⩽ B ⩽ 1 measures the amount of dissipation, and we calculate the successive approximants ƒk(a, B) to the generalized spectral dimension for small (i.e. experimentally feasible) values of k. The crossover properties from the extreme dissipative case (B = 0) to the conservative case (B = 1) are discussed.