  Influence of the weak electric field on the electronic structure of the
Fibonacci superlattice is considered. The electric field produces a nonlinear
dynamics of the energy spectrum of the aperiodic superlattice. Mechanism of the
nonlinearity is explained in terms of energy levels anticrossings. The
multifractal formalism is applied to investigate the effect of weak electric
field on the statistical properties of electronic eigenfunctions. It is shown
that the applied electric field does not remove the multifractal character of
the electronic eigenfunctions, and that the singularity spectrum remains
non-parabolic, however with a modified shape. Changes of the distances between
energy levels of neighbouring eigenstates lead to the changes of the inverse
participation ratio of the corresponding eigenfunctions in the weak electric
field. It is demonstrated, that the local minima of the inverse participation
ratio in the vicinity of the anticrossings correspond to discontinuity of the
first derivative of the difference between marginal values of the singularity
strength. Analysis of the generalized dimension as a function of the electric
field shows that the electric field correlates spatial fluctuations of the
neighbouring electronic eigenfunction amplitudes in the vicinity of
anticrossings, and the nonlinear character of the scaling exponent confirms
multifractality of the corresponding electronic eigenfunctions.
