A Spectral View on Slow Invariant Manifolds in Complex-Time Dynamical Systems

Abstract

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.