Cutting-decimation renormalization for diffusive and vibrational dynamics on fractals

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 tur n out to be invariant under a more complex cutting-decimation transform. In this paper we study in detail the dynamical dimension splitting on these f ractals analyzing the mathematical properties of the cutting-decimation tra nsform. Our results clarify how the splitting arises from the cutting trans form and show that the dynamical dimension degeneracy is a very peculiar co nsequence of exact decimability, (C) 1999 Published by Elsevier Science B.V . All rights reserved.