Chapter 22. Structure of Resonances and Transport in Multidimensional Hamiltonian Dynamical Systems

  1. M. Toda2,
  2. T. Komatsuzaki3,
  3. T. Konishi4,
  4. R. S. Berry5 and
  5. S. A. Rice6
  1. Seiichiro Honjo and
  2. Kunihiko Kaneko

Published Online: 27 JAN 2005

DOI: 10.1002/0471712531.ch22

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

Honjo, S. and Kaneko, K. (2005) Structure of Resonances and Transport in Multidimensional Hamiltonian 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.ch22

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 Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Meguro-ku, Tokyo, 153-8902, 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:

  • Hamiltonian dynamical systems;
  • symplectic map;
  • multi-dimensional systems;
  • transport;
  • diffusion;
  • resonance overlap

Summary

Global diffusion of Hamiltonian dynamical systems is investigated by using a coupled standard maps. Isolated and overlapped resonances are visualized in the frequency space, using local rotation numbers, while Arnold diffusion and diffusion induced by resonance overlaps are distinguished by the residence time distributions at resonance layers. The pathway for fast transport in the phase space is shown to be through overlapped resonances generated by the coupling term. This region plays roles of hubs for transport in the phase space, and enhances the diffusion.