3 citations · 9 across the 9 of their papers we have counts for
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Generalized Liénard systems, singularly perturbed systems, Flow Curvature Method
Jean-Marc Ginoux, Dirk Lebiedz, Jaume Llibre
In his famous book entitled \textit{Theory of Oscillations}, Nicolas Minorsky wrote: "\textit{each time the system absorbs energy the curvature of its trajectory decreases} and \te…
A Spectral View on Slow Invariant Manifolds in Complex-Time Dynamical Systems
Jörn Dietrich, Dirk Lebiedz
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…
On Analytical and Topological Properties of Separatrices in 1-D Holomorphic Dynamical Systems and Complex-Time Newton Flows
Marcus Heitel, Dirk Lebiedz
Separatrices divide the phase space of some holomorphic dynamical systems into separate basins of attraction or 'stability regions' for distinct fixed points. 'Bundling' (high dens…
Characterization of Separatrices in Holomorphic Dynamical Systems
Marcus Heitel, Dirk Lebiedz
Multiple time scales in dynamical systems lead to a bundling of trajectories onto slow invariant manifolds (SIMs). Although they are absent in two-dimensional holomorphic dynamical…
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,…
Covariant geometric characterization of slow invariant manifolds: New concepts and viewpoints
Dirk Lebiedz
We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. Th…