Abstract

n a ly tic a l A p p r o x im a tio n s to T y p e I I I S e p a r a tio n T h r e s h o ld s in P o in c a r e H a lfm a p s The curves Qk, marking the frequency thresholds for type III separation in the parameter space of Poincare halfmaps, are investigated further analytically. In the limit of great values of their argument, the relaxation constant o, all frequency functions Qk are shown to grow algebraically -each with the same exponent being |. Furthermore, a perturbation expansion is presented that yields good results already at a level of approximation where the calculations can be performed