ITERATED FUNCTION SYSTEM AND DIFFUSION IN THE PRESENCE OF DISORDER AND TRAPS

The escape probability xi(x) from a site x of a one-dimensional disord ered lattice with trapping is treated as a discrete dynamical evolutio n by random iterations over nonlinear maps parametrized by the right a nd left jump probabilities. The invariant measure of the dynamics is f ound to be a multifractal. However the measure becomes uniform over th e support when the disorder becomes weak for any nonzero trapping prob ability. Possible implications of our findings to diffusion processes are brought out briefly.