open access

https://hdl.handle.net/2115/54778

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

英語

2013-12

American Institute of Physics

Chaos : an interdisciplinary journal of nonlinear science

23(4)

043107-1-043107-12

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.

学術雑誌論文

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Copyright 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Chaos 23, 043107 (2013) and may be found at http://dx.doi.org/10.1063/1.4824314.

1054-1500

1089-7682

AA10811388