A version of Thirring's approach to the Kolmogorov-Arnold-Moser theorem for quadratic Hamiltonians with degenerate twist

被引：9

作者：

Chandre, C ^{[1
]}

Jauslin, HR ^{[1
]}

机构：

[1] Univ Bourgogne, CNRS, Phys Lab, F-21011 Dijon, France

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 1998年 / 39卷 / 11期

关键词：

D O I：

10.1063/1.532599

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We give a proof of the Kolmogorov-Arnold-Moser (KAM) theorem on the existence of invariant tori for weakly perturbed Hamiltonian systems, based on Thirring's approach for Hamiltonians that are quadratic in the action variables. The main point of this approach is that the iteration of canonical transformations on which the proof is based stays within the space of quadratic Hamiltonians. We show that Thirring's proof for nondegenerate Hamiltonians can be adapted to Hamiltonians with degenerate twist. This case, in fact, drastically simplifies Thirring's proof. (C) 1998 American Institute of Physics. [S0022-2488(98)00611-2].

引用

页码：5856 / 5865

页数：10

共 21 条

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[2]

Arnold V. I., 1963, RUSS MATH SURV, V18, P91, DOI [DOI 10.1070/RM1963V018N06ABEH001143, 10.1070/RM1963v018n06ABEH001143]

[3] A PROOF OF KOLMOGOROV THEOREM ON INVARIANT TORI USING CANONICAL-TRANSFORMATIONS DEFINED BY THE LIE METHOD [J].