Characterization of Separatrices in Holomorphic Dynamical Systems
Dynamical Systems
2019-04-12 v2
Abstract
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.
Cite
@article{arxiv.1904.04616,
title = {Characterization of Separatrices in Holomorphic Dynamical Systems},
author = {Marcus Heitel and Dirk Lebiedz},
journal= {arXiv preprint arXiv:1904.04616},
year = {2019}
}
Comments
2 pages, 2 figures, extended abstract for conference International Workshop on Model Reduction in Reactive Flows (IWMRRF) in Trondheim in 2019