| 汪小明.次线性可逆系统的Aubry-Mather集[J].数学年刊A辑,2015,36(4):355~366 |
| 次线性可逆系统的Aubry-Mather集 |
| Aubry-Mather Sets for Sublinear Reversible Systems |
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| DOI： |
| 中文关键词: 次线性,
可逆系统, Aubry-Mather 集, 无扭周期解 |
| 英文关键词:Sublinear, Reversible systems, Aubry-Mather sets, Unlinked periodic
solutions |
| 基金项目:本文受到国家自然科学基金(No.11461056)和江西省青年自然科学基金(No.20132BAB211008)的资助 |
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| 中文摘要: |
| 通过引进合适的作用\!\!-\!\!角变量变换并结合新的估计方法,
对次线性可逆系统的Poincar\'e 映射, 应用推广的平面可逆系统
的Aubry-Mather 定理, 在系统光滑性为$C^1$的情形下,
获得了一类次线性可逆系统的Aubry-Mather 集存在的充分条件. |
| 英文摘要: |
| In this paper, by introducing an appropriate action-angle variable transforma-
tion and combining with new estimate methods, sufficient conditions are obtained on the
existence of the Aubry-Mather sets to a class of sublinear reversible systems whose smooth-
ness is C1, by virtue of the Aubry-Mather theorem of generalized planar reversible systems
on Poincar′e map of reversible systems. |
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