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

Source: [A Spectral View on Slow Invariant Manifolds in Complex-Time Dynamical Systems](<https://www.sota2.com/research/paper/68fa3b0a1e209131ce8cf8a2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T00:23:50.854Z

Authors: J\\"orn Dietrich, Dirk Lebiedz

Published: 2019-11-26T13:17:55.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1912.00748>)

[PDF](<https://arxiv.org/pdf/1912.00748.pdf>)