Non-degeneracy conditions in KAM theory

被引：6
|
作者：
Hanssmann, Heinz [1 ]
机构：
[1] Univ Utrecht, Math Inst, NL-3508 TA Utrecht, Netherlands
来源：
INDAGATIONES MATHEMATICAE-NEW SERIES | 2011年 / 22卷 / 3-4期
关键词：
INTEGRABLE HAMILTONIAN-SYSTEMS; LOWER-DIMENSIONAL TORI; IMPLICIT FUNCTION THEOREMS; SMALL DIVISOR PROBLEMS; QUASI-PERIODIC TORI; HOPF-BIFURCATION; INVARIANT TORI; PERSISTENCE; PERTURBATIONS; STABILITY;
D O I：
10.1016/j.indag.2011.09.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Persistence of invariant tori in a perturbed dynamical system requires two kinds of conditions to be met. A strong non-resonance condition ensures a dense quasi-periodic orbit on both the unperturbed and the perturbed torus. A non-degeneracy condition enforces a sufficiently large subset of the unperturbed tori to be non-resonant and thus yields persistence. In the past 60 years various such conditions have been formulated and a number of them are reviewed here. (C) 2011 Royal Netherlands Academy of Arts and Sciences. Published by Elsevier B.V. All rights reserved.
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页码：241 / 256
页数：16
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