MULTIFRACTALITY OF PROBABILITY MEASURE ON ENERGY-SPECTRUM SUPPORTS

We have studied quadric type energy (frequency) recursion relations re sulting from fractal lattices. We found that the allowed energy interv als in successive levels form two similar two-scale Cantor sets. If we imagine the iterating procedure as a dynamical process, the iterating results in different levels generate a ''time'' sequence, and we can introduce an equal probability measure p(i) on a Cantor set and constr uct, following Helsey et al. [Phys. Rev. A 33, 1141 (1986)], a partiti on function GAMMA(q, tau) = SIGMA(i)p(i)q/l(i)tau; finally, we obtain D(q)-q and f(alpha)-alpha curves. A number of exactly soluable example s are investigated.