Detecting invariant manifolds as stationary Lagrangian coherent structures in autonomous dynamical systems

• Teramoto, Hiroshi

• Haller, George

• Komatsuzaki, Tamiki

抄録

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.

収録刊行物

• Chaos : an interdisciplinary journal of nonlinear science

  Chaos : an interdisciplinary journal of nonlinear science 23 (4), 043107-1-043107-12, 2013-12

  American Institute of Physics

詳細情報

• CRID: 1050845763945760384
• NII論文ID: 120005385313
• NII書誌ID: AA10811388
• ISSN: 10897682
• ISSN: 10541500
• HANDLE: 2115/54778
• 本文言語コード: en
• 資料種別: journal article
• データソース種別:
  • IRDB
  • CiNii Articles