  Many real-analytic flows, e.g. in chemical kinetics, share a multiple time
scale spectral structure. The trajectories of the corresponding dynamical
systems are observed to bundle near so-called slow invariant manifolds (SIMs),
which are usually addressed in a singular perturbation context. This work
exploits the analytic structure of the involved vector fields and presents
observations that connect one dimensional slow invariant manifolds to the
imaginary-time spectral structure of Riemann surfaces in analytic continuations
of dynamical systems to complex time.
