  We study multifractal properties of wave functions for a one-parameter family
of quantum maps displaying the whole range of spectral statistics intermediate
between integrable and chaotic statistics. We perform extensive numerical
computations and provide analytical arguments showing that the generalized
fractal dimensions are directly related to the parameter of the underlying
classical map, and thus to other properties such as spectral statistics. Our
results could be relevant for Anderson and quantum Hall transitions, where wave
functions also show multifractality.
