The backward phase flow method for the Eulerian finite time Lyapunov exponent computations

Shing-Yu Leung

Numerical Analysis and Scientific Computing mathscidoc:1912.43185

Chaos: An Interdisciplinary Journal of Nonlinear Science, 23, (4), 043132, 2013.12
We propose a simple Eulerian approach to compute the moderate to long time flow map for approximating the Lyapunov exponent of a (periodic or aperiodic) dynamical system. The idea is to generalize a recently proposed backward phase flow method which is specially designed for long time level set propagation. Unlike the original phase flow method or the backward phase flow method, which is applicable only to autonomous systems, the current approach can also be applied to any time-dependent (periodic or aperiodic) flow. We will discuss the stability of the proposed method. Numerical examples will be given to demonstrate the effectiveness of the algorithm.
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@inproceedings{shing-yu2013the,
  title={The backward phase flow method for the Eulerian finite time Lyapunov exponent computations},
  author={Shing-Yu Leung},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112817554815745},
  booktitle={Chaos: An Interdisciplinary Journal of Nonlinear Science},
  volume={23},
  number={4},
  pages={043132},
  year={2013},
}
Shing-Yu Leung. The backward phase flow method for the Eulerian finite time Lyapunov exponent computations. 2013. Vol. 23. In Chaos: An Interdisciplinary Journal of Nonlinear Science. pp.043132. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112817554815745.
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