Unraveling chaotic attractors of walking droplets by symmetry reduction

Droplets bouncing on the vibrating bath of the same fluid were shown to exhibit chaotic dynamics in the presence of a confining radial force and sufficiently high vibration amplitude (Tambasco et al., Chaos 25, 103107 (2016)). Complex dynamics in these systems arise as a result of their "memory": At an instance, the surface of the bath is shaped by the waves generated at previous bounces of the droplet; thus, the bath surface "remembers" the droplet's trajectory. In addition, the continuous rotation symmetry of these systems further complicates their dynamics since each generic solution has infinitely many symmetry-copies. We will present a continuous symmetry-reduction scheme for walking droplets that can be applied in both numerical and laboratory settings. We will demonstrate with examples that the symmetry-reduction reveals surprisingly simple chaotic attractors and yields an intuitive picture of global dynamics of the system.