  We show that scattering from the boundary of static, higher-order topological
insulators (HOTIs) can be used to simulate the behavior of (time-periodic)
Floquet topological insulators. We consider D-dimensional HOTIs with gapless
corner states which are weakly probed by external waves in a scattering setup.
We find that the unitary reflection matrix describing back-scattering from the
boundary of the HOTI is topologically equivalent to a (D-1)-dimensional
nontrivial Floquet operator. To characterize the topology of the reflection
matrix, we introduce the concept of `nested' scattering matrices. Our results
provide a route to engineer topological Floquet systems in the lab without the
need for external driving. As benefit, the topological system does not to
suffer from decoherence and heating.
