Spatiotemporal dynamics of scattering exceptional points

Exceptional points (EPs) offer new routes to control wave-matter interactions in non-Hermitian systems. Whereas conventional EPs arise in Hamiltonians and mark eigenstate coalescence, scattering EPs recast them in input-output responses for free-space wave control. Yet the rich topology of EPs is largely concealed in steady-state observables, exhibiting similar asymmetric patterns governed by identical Jordan-block forms. Here we exploit scattering as an evolving process in space and time to resolve spatiotemporal dynamics. We establish a cross-domain mapping from momentum-frequency to space-time, connecting static EPs to dynamic scattering singularities. By projecting a unitary scattering matrix onto lower-dimensional subspaces, EP topology is imprinted into a wave packet as a spatiotemporal vortex (STV), whose phase singularity is anchored to the EP and carries its quantized topological charge. In a liquid-surface-wave platform, we observe a charge-1 STV and a disintegrated charge-2 STV, generated by distinct EPs in a single device. Our work links fixed exceptional topology to dynamic wave topology, establishing a framework for spatiotemporal wave control.