# State space geometry of the chaotic pilot-wave hydrodynamics

## TL;DR

This paper develops a symmetry-reduced dynamical systems framework to analyze the chaotic behavior of a bouncing droplet in a central potential, revealing bifurcations, chaos onset, and angular momentum reversals.

## Contribution

It introduces a rotation symmetry reduction method applied to pilot-wave hydrodynamics, enabling detailed analysis of bifurcations and chaos in the system.

## Key findings

- Identification of local bifurcations leading to chaos
- Description of chaotic region emergence and merging bifurcations
- Observation of spontaneous angular momentum sign changes

## Abstract

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).