哈密顿系统不变环面的通有超指数稳定性
Generic super-exponential stability of invariant tori in Hamiltonian systems
摘要：
在这篇文章中，我们考虑的解决方案开始接近一些线性稳定不变环面的分析哈密顿系统，我们证明了稳定性的结果为超指数长的时间间隔，在一般条件下。该证明结合了经典的伯克霍夫范式和作者和L.尼德曼在另一份报纸上。我们将主要关注椭圆不动点的邻域，其他情况完全相似。
英文摘要：
In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.
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