Chapter 7. Global Aspects of Chemical Reactions in Multidimensional Phase Space

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

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch7

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

Toda, M. (2005) Global Aspects of Chemical Reactions in Multidimensional Phase Space, 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.ch7

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. Physics Department, Nara Women's University, Nara, 630-8506, 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:

  • singular perturbation;
  • normally hyperbolic invariant manifold;
  • Melnikov integral;
  • Arnold diffusion;
  • tangency;
  • crisis

Summary

Understanding reaction processes requires the study of global aspects of the phase space in multi-dimensional chaotic dynamics. In order to proceed this study, we propose to take the following strategy. Our strategy consists of three stages. First, we simplify description of the dynamics locally in the phase space. This is done in an analogous and extended way of the conventional transition state theory. Second, we study how the local dynamics in different regions of the phase space are related to each other. Thus, global structures of the phase space are our target at this stage. Third, bifurcation in the global structures is the aim of our study.