  We consider the motion of a droplet bouncing on a vibrating bath of the same
fluid in the presence of a central potential. We formulate a rotation
symmetry-reduced description of this system, which allows for the
straightforward application of dynamical systems theory tools. As an
illustration of the utility of the symmetry reduction, we apply it to a model
of the pilot-wave system with a central harmonic force. We begin our analysis
by identifying local bifurcations and the onset of chaos. We then describe the
emergence of chaotic regions and their merging bifurcations, which lead to the
formation of a global attractor. In this final regime, the droplet's angular
momentum spontaneously changes its sign as observed in the experiments of
Perrard et al. (Phys. Rev. Lett., 113(10):104101, 2014).
