Destruction of Lagrangian torus for positive definite Hamiltonian systems

Chong-Qing Cheng; Lin Wang

Destruction of Lagrangian torus for positive definite Hamiltonian systems

Dynamical Systems 2012-11-29 v1 Functional Analysis

Authors: Chong-Qing Cheng , Lin Wang

Abstract

For an integrable Hamiltonian $H_0=1/2\sum_{i=1}^dy_i^2$ $(d\geq 2)$ , we show that any Lagrangian torus with a given unique rotation vector can be destructed by arbitrarily $C^{2d-\delta}$ -small perturbations. In contrast with it, it has been shown that KAM torus with constant type frequency persists under $C^{2d+\delta}$ -small perturbations.

Keywords

Lagrangian torus destruction positive definite Hamiltonian systems KAM theory small perturbations rotation vector

Cite

@article{arxiv.1211.6480,
  title  = {Destruction of Lagrangian torus for positive definite Hamiltonian systems},
  author = {Chong-Qing Cheng and Lin Wang},
  journal= {arXiv preprint arXiv:1211.6480},
  year   = {2012}
}

Comments

accepted by Geometric and Functional Analysis (GAFA). arXiv admin note: substantial text overlap with arXiv:1208.2840

Destruction of Lagrangian torus for positive definite Hamiltonian systems

Abstract

Keywords

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