论文标题
几乎可以集成的哈密顿系统的部分的灵活性
Flexibility of sections of nearly integrable Hamiltonian systems
论文作者
论文摘要
给定对$ d^{2n}（n \ geq 1）$的任何符号术，该$是$ c^{\ infty} $接近身份，以及任何完全可以集成的哈密顿系统$φ^t_h $在适当的维度中，我们构造了$ c^{\ infty} $ pertterian的本地化，例如，$ h $ h $ h $ h $ h $ h $ h $ h $ h $ h hamilton' “意识到”符号呈现。作为一种（激励的）应用，我们表明，任何完全可以整合的哈密顿系统都有任意小的扰动，这些扰动是熵的非强度（尤其是在一组积极度量上表现出双曲线行为）。
Given any symplectomorphism on $D^{2n} (n\geq 1)$ which is $C^{\infty}$ close to the identity, and any completely integrable Hamiltonian system $Φ^t_H$ in the proper dimension, we construct a $C^{\infty}$ perturbation of $H$ such that the resulting Hamiltonian flow contains a "local Poincaré section" that "realizes" the symplectomorphism. As a (motivating) application, we show that there are arbitrarily small perturbations of any completely integrable Hamiltonian system which are entropy non-expansive (and, in particular, exhibit hyperbolic behavior on a set of positive measure).
