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arXiv · 1904.04613

Analytic continuation and differential geometry views on slow manifolds and separatrices

Dirk Lebiedz·Jörn Dietrich·Marcus Heitel·Johannes Poppe
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Abstract

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.

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Dirk Lebiedz, Jörn Dietrich, Marcus Heitel, Johannes Poppe. 2019-04-09. Analytic continuation and differential geometry views on slow manifolds and separatrices. https://arxiv.org/abs/1904.04613

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