Quasiperiodic and chaotic states in the ding-dong model for N=3

The system considered is a chain of spheres bound harmonically to equidista nt points and colliding elastically. This is the so-called "ding-dong" mode l of Prosen and Robnik, 1992. For 3 spheres we investigate the transition f rom chaos to quasiperiodicity in a numerical experiment. The character of m otion is determined by calculation of the box counting fractal dimension of the t(n + 1) versus t(n) plot, where t(n) is a time between an nth and an (n + 1)th collision between spheres. The result is that the transition occu rs at many regions of the phase space for all values of the total energy. W e conclude that, in the contrast to what was suggested by other authors, th e character of motion cannot be deduced from one parameter.