Iterated Function System and diffusion in the presence of traps

The escape probability ξx from a site x of a one-dimensional disordered lattice with trapping is treated as a discrete dynamical evolution by random iterations over nonlinear maps parametrized by the right and left jump probabilities. The invariant measure of the dynamics is found to be a multifractal. However the measure becomes uniform over the support when the disorder becomes weak for any nonzero trapping probability. Possible implications of our findings to diffusion processes are brought out briefly.