  Eigenmode coalescence imparts remarkable properties to non-hermitian time
evolution, culminating in a purely non-hermitian spectral degeneracy known as
an exceptional point (EP). Here, we revisit time evolution at the EP and
classify two-level non-hermitian Hamiltonians in terms of the M\"obius group.
We then leverage that classification to study dynamical EP encircling, by
applying it to periodically-modulated (Floquet) Hamiltonians. This reveals that
Floquet non-hermitian systems exhibit rich physics whose complexity is not
captured by an EP-encircling rule. For example, Floquet EPs can occur without
encircling and vice-versa. Instead, we show that the elaborate interplay
between non-hermitian and modulation instabilities is better understood through
the lens of parametric resonance.
