Generalized dimensions of Feigenbaum's attractor from   renormalization-group functional equations
  A method is suggested for the computation of the generalized dimensions of fractal attractors at the period-doubling transition to chaos. The approach is based on an eigenvalue problem formulated in terms of functional equations, with a coefficient expressed in terms of Feigenbaum's universal fixed-point function. The accuracy of the results is determined only by precision of the representation of the universal function. 
S.P.Kuznetsov and A.H.Osbaldestin