Multifractality of nonlinear iterative processes

The Havlin-Bunde multifractal hypothesis Physica D 38:184 (1989)] is expanded (in the form of the dimension-invariance approach) to nonlinear iterative (recursion) processes such as dielectric breakdown, phase transitions from periodic attractors to chaos, and cascades in turbulence. Comparison with model and laboratory data of different authors shows that for strong nonlinearity the dimension invariance is broken