THE EFFECT of WEAK DISSIPATION IN TWO-DIMENSIONAL MAPPING

Abstract

The influence of weak dissipation and its consequences in a two-dimensional mapping are studied. The mapping is parametrized by an exponent gamma in one of the dynamical variables and by a parameter delta which denotes the amount of the dissipation. It is shown that for different values of gamma the structure of the phase space of the nondissipative model is replaced by a large number of attractors. The approach to the attracting fixed point is characterized both analytically and numerically. The attracting fixed point exhibits a very complicated basin of attraction.