  Fractalization of torus and its transition to chaos in a quasi-periodically
forced logistic map is re-investigated in relation with a strange nonchaotic
attractor, with the aid of functional equation for the invariant curve.
Existence of fractal torus in an interval in parameter space is confirmed by
the length and the number of extrema of the torus attractor, as well as the
Fourier mode analysis. Mechanisms of the onset of fractal torus and the
transition to chaos are studied in connection with the intermittency.
