Chapter 25. Finite-Time Lyapunov Exponents in Many-Dimensional Dynamical Systems

  1. M. Toda2,
  2. T. Komatsuzaki3,
  3. T. Konishi4,
  4. R. S. Berry5 and
  5. S. A. Rice6
  1. Teruaki Okushima

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch25

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130

How to Cite

Okushima, T. (2005) Finite-Time Lyapunov Exponents in Many-Dimensional Dynamical Systems, in Geometric Structures of Phase Space in Multidimensional Chaos: Applications to Chemical Reaction Dynamics in Complex Systems, Volume 130 (eds M. Toda, T. Komatsuzaki, T. Konishi, R. S. Berry and S. A. Rice), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471712531.ch25

Editor Information

  1. 2

    Physics Department, Nara Women's University, Nara, 630-8506, Japan

  2. 3

    Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe, 657-8501, Japan

  3. 4

    Department of Physics, Nagoya University, Nagoya, 464-8602, Japan

  4. 5

    Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, USA

  5. 6

    Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

Author Information

  1. Department of Physics, Tokyo Metropolitan University, Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan

Publication History

  1. Published Online: 27 JAN 2005
  2. Published Print: 21 JAN 2005

Book Series:

  1. Advances in Chemical Physics

Book Series Editors:

  1. Stuart A. Rice

Series Editor Information

  1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 USA

ISBN Information

Print ISBN: 9780471711582

Online ISBN: 9780471712534

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Keywords:

  • finite-time Lyapunov exponents and vectors;
  • many-dimensional dynamics;
  • non-hyperbolic system;
  • numerical method;
  • correction to QR method;
  • ordered motion

Summary

We present a new relatively simple method for computing finite-time Lyapunov exponents and vectors via developing iterative corrections, which is applicable to systems with degenerate Lyapunov spectra in contrast to the existing methods. Applying our method to a generic many-dimensional oscillator system, we obtain a clear evidence that qualitatively different Lyapunov instabilities, of exponential and linear time-dependences, coexist in a trajectory, which enables us to determine the lifetimes of ordered motions. These results could not be obtained without the novel corrections in general.