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arXiv:1904.04616 [math.DS]AbstractReferencesReviewsResources

Characterization of Separatrices in Holomorphic Dynamical Systems

Marcus Heitel, Dirk Lebiedz

Published 2019-04-09Version 1

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 systems, a bundling of orbits is often observed as well. They bundle onto special trajectories called separatrices. We apply numerical methods for the approximation of SIMs to holomorphic flows and show how a separatrix between two regions of periodic orbits can be characterized topologically. Complex time reveals a new perspective on holomorphic dynamical systems.

Comments: 2 pages, 2 figures, extended abstract for conference International Workshop on Model Reduction in Reactive Flows (IWMRRF) in Trondheim in 2019
Categories: math.DS
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