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Communications in Mathematical Physics

, Volume 203, Issue 2, pp 385–419 | Cite as

Lower Dimensional Invariant Tori in the Regions of Instability for Nearly Integrable Hamiltonian Systems

  • Chong-Qing Cheng

Abstract:

Consider a Hamiltonian system of KAM type, H(p,q)=N(p)+P(p,q), with n degrees of freedom (n>2), where the Hessian of N is nondegenerate. For one resonance condition <I,N p >=0, \ (I∈ℤ n ), there is an immersed (n−1) dimensional submanifold ? in action variable space, where almost every point corresponds to a resonant torus for the unperturbed system, which is foliated by (n−1) dimensional ergodic components. It is shown in this paper that there is a subset of ? with positive (n−1)-dim Lebesgue measure, such that for each resonant torus corresponding to a point in this set at least two (n−1)-dimensional tori can survive perturbations. Generically, one is hyperbolic and the other one is elliptic.

Keywords

Hamiltonian System Resonance Condition Variable Space Unperturbed System Lower Dimensional 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Chong-Qing Cheng
    • 1
  1. 1.Department of Mathematics, Nanjing University, Nanjing 210093, China.¶E-mail: chengcq@nju.edu.cnCN

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