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Weak instabilities in many-dimensional Hamiltonian systems

Franco Vivaldi*

Franco Vivaldi*

  • School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332

  • *Now at Department of Applied Mathematics, Queen Mary College, University of London, Mile End Road, London, E1 4NS, England.
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Rev. Mod. Phys. 56, 737 – Published 1 October, 1984

DOI: https://doi.org/10.1103/RevModPhys.56.737

Abstract

The problem of long-time predictions in many-dimensional Hamiltonian systems is examined. Some geometrical methods of nonlinear dynamics are reviewed, and applied to the study of a class of instabilities that are peculiar of systems with more than two degrees of freedom. These are called "weak instabilities," since they manifest themselves only after a long time. A qualitative analysis of the weak instability induced by slow parametric modulation (the modulational diffusion) is developed. The relevance of these phenomena to the problem of stability of charged particles in accelerators and storage rings is discussed.

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Rev. Mod. Phys. 56, 737– Published 1 October, 1984

    © 1984 American Physical Society

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