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arXiv · 1211.6480

Destruction of Lagrangian torus for positive definite Hamiltonian systems

Chong-Qing Cheng·Lin Wang
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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.

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Chong-Qing Cheng, Lin Wang. 2012-11-27. Destruction of Lagrangian torus for positive definite Hamiltonian systems. https://arxiv.org/abs/1211.6480

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