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arXiv · 1904.04616

Characterization of Separatrices in Holomorphic Dynamical Systems

Marcus Heitel·Dirk Lebiedz
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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.

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Marcus Heitel, Dirk Lebiedz. 2019-04-09. Characterization of Separatrices in Holomorphic Dynamical Systems. https://arxiv.org/abs/1904.04616

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