Lyapunov unstable elliptic equilibria
Lyapunov unstable elliptic equilibria
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DOI：
10.1090/jams/997
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发表时间：
2018-09
影响因子：
3.9
通讯作者：
B. Fayad
中科院分区：
文献类型：
--
作者：
B. Fayad
介绍了一种新的三自由度哈密顿流的扩散机制，它是由椭圆平衡邻域出发的。因此，我们得到了r2上的显式实数完整哈密顿量\mathbb R{^}2d{, d≥4d }\geq 4，它具有具有任意选择的频率向量的Lyapunov不稳定椭圆平衡，其坐标不都是相同的符号。对于非谐振频率矢量，我们的例子在平衡状态下都具有发散的Birkhoff范式。在r4 \mathbb R{^4上，我们给出了具有任意选择的非谐振频率矢量和发散Birkhoff范式的平衡的实全哈密顿量的显式例子。}
A new diffusion mechanism from the neighborhood of elliptic equilibria for Hamiltonian flows in three or more degrees of freedom is introduced. We thus obtain explicit real entire Hamiltonians on R 2 d \mathbb {R}^{2d} , d ≥ 4 d\geq 4 , that have a Lyapunov unstable elliptic equilibrium with an arbitrary chosen frequency vector whose coordinates are not all of the same sign. For non-resonant frequency vectors, our examples all have divergent Birkhoff normal form at the equilibrium. On R 4 \mathbb {R}^4 , we give explicit examples of real entire Hamiltonians having an equilibrium with an arbitrary chosen non-resonant frequency vector and a divergent Birkhoff normal form.