Characterization of Separatrices in Holomorphic Dynamical Systems

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.

2 pages, 2 figures, extended abstract for conference International Workshop on Model Reduction in Reactive Flows (IWMRRF) in Trondheim in 2019