CIRCLE MAPS WITH SYMMETRY-BREAKING PERTURBATIONS

Renormalization group methods are used to describe the transition to chaos that occurs in dissipative quasiperiodic systems in the presence of a small subharmonic perturbation. This is accomplished by studying the circle map with the symmetry theta --> theta + 2-pi/n, and looking at crossover exponents for perturbations obeying the usual 2-pi symmetry. In order to interpret these exponents, the standard renormalization group analysis must be extended to include extra functions. This has been worked out in detail for the case n = 2.