Multifurcations at the origin of Zaslavsky's map with twist

Abstract

As the nonlinear parameter, k of Zaslavsky's map with twist increases, chains of periodic points are born simultaneously at the origin and move outwards. The positions of the periodic points as a function of k is investigated, and in a limited number of cases an analytic result is found. When k is very small, it is found that there is a universal relation for the radius of the periodic points as a function of the nonlinear parameter.