Chiral-symmetric Topological Origin of Nonlinear Fixed Points

Particle-hole symmetry and chiral symmetry play a pivotal role in multiple areas of physics, yet they remain un-studied in systems with nonlinear interactions that are beyond Kerr-type. Here, we establish these two non-spatial symmetries in systems with strong and general nonlinear interactions. Chiral symmetry ensures the quantization of the Berry phase of nonlinear normal modes and categorizes the topological phases of nonlinear dynamics. We show edge modes that serve as topologically protected fixed points of chiral-symmetric nonlinear dynamics. Our theoretical framework paves the way towards the topological classification of general nonlinear dynamics.