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Regions of Applicability of Aubry-Mather Theory for Non-convex Hamiltonian

Regions of Applicability of Aubry-Mather Theory for Non-convex Hamiltonian
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摘要 Herman constructed an autonomous system of two degrees of freedom which says that in non-convex situations, oscillations do happen and Aubry-Mather Theory cannot apply (see the results due to W. F. Chen in 1992). In this paper, it is shown that although the orbits could visit a region far away from the initial point in phase space, they can only exist in some fixed regions in I = (I1 , I2 ) plane. Moreover, Aubry-Mather Theory can be applied outside the regions.
作者 Min ZHOU Binggui ZHONG
机构地区 Department of Mathematics
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2011年第4期605-614,共10页 数学年刊（B辑英文版）
基金 Project Supported by the Graduate Student Research Fellowship of Jiangsu Province of China (No.CX10B_002Z)
关键词 Twist map Aubry-Mather Theory Non-convex Hamiltonian 哈密顿理论 非凸 适用性 自治系统 自由度 相空间 初始点
分类号 O316 [理学—一般力学与力学基础] TP13 [自动化与计算机技术—控制理论与控制工程]
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参考文献21

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Chinese Annals of Mathematics,Series B
2011年 第4期

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