Nekhoroshev 定理对周期 Toda 晶格。

Nekhoroshev theorem for the periodic Toda lattice.

机构信息

Institut für Mathematik, Universität Zurich, Zürich, Switzerland.

出版信息

Chaos. 2009 Sep;19(3):033120. doi: 10.1063/1.3196783.

DOI:10.1063/1.3196783

PMID:19792000

Abstract

The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space (2000 Mathematics Subject Classification: 37J35, 37J40, 70H06).

摘要

N 点周期 Toda 晶格与 N-1 个耦合谐振子的两参数族全局辛同胚。作用变量填充了 R（N-1）的整个正象限。我们证明了在正象限的内部以及原点的邻域中，Toda 哈密顿量是严格凸的，因此 Nekhoroshev 定理适用于（几乎）相空间的所有部分（2000 数学主题分类：37J35、37J40、70H06）。