  Two dimensional electrons in weakly disordered high Landau levels are
considered. The current-field response in the presence of a strong microwave
field, is computed. The disordered Floquet evolution operator allows us to
treat the short range disorder perturbatively, at any strength of electric
fields. A simplifying Random Matrix Approximation reproduces the broadened
Landau levels density of states and structure factor. We derive the magnitude
of the Microwave Induced Resistivity Oscillations. The disorder short
wavelength cut-off determines the non-linear electric fields of the Zero
Resistance State and the Hall Induced Resistivity Oscillations. We discuss
wider implications of our results on experiments and other theories.
