Universality and scaling in the circle map under external periodic driving

Abstract

We investigate scaling properties of а neighborhood of the «golden mean» critical point in the circle map in presence of external periodic forcing upon the system. We consider such perturbations of the fixed point of the Feigenbaum-Kadanoff-Shenker renormalization group equation, which are initiated by periodic forcing. We show that, depending upon the frequency of external forcing, two types of scaling behavior can be observed. The first (P-type) 18 associated with periodic repetition of the structures of dynamical regimes in parameter space under subsequent scaling transformations. For the second case (Q-type of scaling) quasiperiodic behavior of structures in the parameter space takes place. The both types of scaling are illustrated by parameter-space diagrams for re-scaled Lyapunov exponents.