  The nonlinear climbing sine map is a nonhyperbolic dynamical system
exhibiting both normal and anomalous diffusion under variation of a control
parameter. We show that on a suitable coarse scale this map generates an
oscillating parameter-dependent diffusion coefficient, similarly to hyperbolic
maps, whose asymptotic functional form can be understood in terms of simple
random walk approximations. On finer scales we find fractal hierarchies of
normal and anomalous diffusive regions as functions of the control parameter.
By using a Green-Kubo formula for diffusion the origin of these different
regions is systematically traced back to strong dynamical correlations.
Starting from the equations of motion of the map these correlations are
formulated in terms of fractal generalized Takagi functions obeying generalized
de Rham-type functional recursion relations. We finally analyze the measure of
the normal and anomalous diffusive regions in the parameter space showing that
in both cases it is positive, and that for normal diffusion it increases by
increasing the parameter value.
