2019/04/09 by Marcus Heitel, Heitel, Marcus, Dirk Lebiedz +1
Physics and Astronomy · Mathematics · Computer Science · #Quantum chaos and dynamical systems #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1904.04616
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.