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math.DS2024
Sensitivities in complex-time flows: phase transitions, Hamiltonian structure and differential geometry
Dirk Lebiedz, Johannes Poppe
Reminiscent of physical phase transitions separatrices divide the phase space of dynamical systems with multiple equilibria into regions of distinct flow behavior and asymptotics.…
math.DS2019
On Differential Geometric Formulations of Slow Invariant Manifold Computation: Geodesic Stretching and Flow Curvature
Johannes Poppe, Dirk Lebiedz
The theory of slow invariant manifolds (SIMs) is the foundation of various model-order reduction techniques for dissipative dynamical systems with multiple time-scales, e.g. in che…
math.DS2019
Analytic continuation and differential geometry views on slow manifolds and separatrices
Dirk Lebiedz, Jörn Dietrich, Marcus Heitel +1
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,…