  We start from a mechano-chemical analogy considering the time evolution of a
homogeneous chemical reaction modeled by a nonlinear dynamical system (ordinary
differential equation, ODE) as the movement of a phase space point on the
solution manifold such as the movement of a mass point in curved spacetime.
Based on our variational problem formulation \cite{Lebiedz2011} for slow
invariant manifold (SIM) computation and ideas from general relativity theory
we argue for a coordinate free analysis treatment \cite{Heiter2018} and a
differential geometry formulation in terms of geodesic flows \cite{Poppe2019}.
In particular, we propose analytic continuation of the dynamical system to the
complex time domain to reveal deeper structures and allow the application of
the rich toolbox of Fourier and complex analysis to the SIM problem.
