On the existence of invariant tori in nearly-integrable Hamiltonian systems with finitely differentiable perturbations

被引：12

作者：

Albrecht, J. ^{[1
]}

机构：

[1] Friedrichshof, D-50997 Cologne, Germany

来源：

REGULAR & CHAOTIC DYNAMICS | 2007年 / 12卷 / 03期

关键词：

nearly integrable Hamiltonian systems; KAM theory; perturbations; small divisors; Celestial Mechanics; quasi-periodic motions; invariant tori; trigonometric approximation in several variables; Holder condition;

D O I：

10.1134/S1560354707030033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of invariant tori in Hamiltonian systems, which are analytic and integrable except a 2n-times continuously differentiable perturbation (n denotes the number of the degrees of freedom), provided that the moduli of continuity of the 2n-th partial derivatives of the perturbation satisfy a condition of finiteness ( condition on an integral), which is more general than a Holder condition. So far the existence of invariant tori could be proven only under the condition that the 2n-th partial derivatives of the perturbation are Holder continuous.

引用

页码：281 / 320

页数：40