  Recently, we pointed out that on a class on non exactly decimable fractals
two different parameters are required to describe diffusive and vibrational
dynamics. This phenomenon we call dynamical dimension splitting is related to
the lack of exact decimation invariance for these structures, which turn out to
be invariant under a more complex cutting-decimation transform. In this paper
we study in details the dynamical dimension splitting on these fractals
analyzing the mathematical properties of the cutting-decimation transform. Our
results clarify how the splitting arises from the cutting transform and show
that the dynamical dimension degeneration is a very peculiar consequence of
exact decimability.
