TRANSITIONS TO BUBBLING OF CHAOTIC SYSTEMS

Certain dynamical systems exhibit a phenomenon called bubbling, whereb y small perturbations induce intermittent bursting. In this Letter we show that, as a parameter is varied through a critical value, the tran sition to bubbling can be ''hard'' (the bursts appear abruptly with la rge amplitude) or ''soft'' (the maximum burst amplitude increases cont inuously from zero), and that the presence or absence of symmetry in t he unperturbed system has a fundamental effect on these transitions. T hese results are confirmed by numerical and physical experiments.