title: Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems.
abstract: Normally hyperbolic invariant manifolds (NHIMs) are well-known organizing centers of the dynamics in the phase space of a nonlinear system. Locating such manifolds in systems far from symmetric or integrable, however, has been an outstanding challenge. Here, we develop an automated detection method for codimension-one NHIMs in autonomous dynamical systems. Our method utilizes Stationary Lagrangian Coherent Structures (SLCSs), which are hypersurfaces satisfying one of the necessary conditions of a hyperbolic LCS, and are also quasi-invariant in a well-defined sense. Computing SLCSs provides a quick way to uncover NHIMs with high accuracy. As an illustration, we use SLCSs to locate two-dimensional stable and unstable manifolds of hyperbolic periodic orbits in the classic ABC flow, a three-dimensional solution of the steady Euler equations.
authors.affiliation: Molecule & Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan.
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Teramoto
authors.affiliation: Institute for Mechanical Systems, ETH Zürich, CLA J.27, Tannenstrasse 3, 8092 Zürich, Switzerland.
authors.forename: George
authors.initials: G
authors.lastname: Haller
authors.affiliation: Molecule & Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan.
authors.forename: Tamiki
authors.initials: T
authors.lastname: Komatsuzaki
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical