Physical meaning for Mandelbrot and Julia sets

We consider the dynamics of a kicked charged particle moving in a double-well potential and a time-dependent magnetic field. In certain cases the stroboscopic dynamics reduces to the complex logistic map, thus providing physical meaning for the Mandelbrot set. In other cases we obtain iterated function systems consisting of the inverse complex logistic map, thus providing physical meaning for Julia sets. Our approach can be generalized to complex mappings with a maximum of order q. (C)1999 Elsevier Science B.V. All rights reserved.