Chapter 21. Slow Dynamics in Multidimensional Phase Space: Arnold Model Revisited

  1. M. Toda1,
  2. T. Komatsuzaki2,
  3. T. Konishi3,
  4. R. S. Berry4 and
  5. S. A. Rice5
  1. Tetsuro Konishi

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch21

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

Konishi, T. (2005) Slow Dynamics in Multidimensional Phase Space: Arnold Model Revisited, 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.ch21

Editor Information

  1. 1

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

  2. 2

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

  3. 3

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

  4. 4

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

  5. 5

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

Author Information

  1. Department of Physics, Nagoya University, Nagoya, 464-8602, 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:

  • Arnold diffusion;
  • slow dynamics;
  • temporal correlation;
  • multi-precision computation

Summary

“Arnold diffusion” is numerically observed by performing extremely high precision computation. Singular dependence (i.e., extremely small displacement rate) on the magnitude of hyperbolicity is confirmed. Temporal correlation of the displacement of action variable implies that the process, although called “Arnold diffusion”, is not diffusive.