|本期目录/Table of Contents|

[1]张晶,黄土森.一类退化非线性微分方程的正规形计算[J].浙江理工大学学报,2017,37-38(自科6):866-873.
 ZHANG Jing,HUANG Tusen.Computation of Normal Forms for a Class of Degenerate Nonlinear Differential Equations[J].Journal of Zhejiang Sci-Tech University,2017,37-38(自科6):866-873.
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一类退化非线性微分方程的正规形计算()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第37-38卷
期数:
2017年自科6期
页码:
866-873
栏目:
出版日期:
2017-11-10

文章信息/Info

Title:
Computation of Normal Forms for a Class of Degenerate Nonlinear Differential Equations
文章编号:
1673-3851 (2017) 06-0866-08
作者:
张晶黄土森
浙江理工大学理学院,杭州 310018
Author(s):
ZHANG Jing HUANG Tusen
School of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
退化非线性微分方程正规形保守耗散分解
分类号:
O175.14
文献标志码:
A
摘要:
对于退化非线性微分方程,给出了其主微分方程的保守耗散分解,并证明了这种分解的几个性质。利用这些性质,把求定义在齐次向量场空间上的同调算子值域补空间,转化为求定义在齐次多项式空间上李导数算子值域补空间。在主微分方程是哈密尔顿的并且哈密尔顿函数在复多项式环C[x,y]上的因式仅为单因式的假设下,为求得系统的正规形,只需求有限个定义在齐次多项式空间上的李导数算子值域补空间,并给出递推公式。用该方法可求出一类具有广义Hopf奇点的正规形,并利用李三角形方法给出正规形与原微分方程系数之间的关系。

参考文献/References:

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[3] ASHKENAZI M, CHOW S N. Normal forms near critical points for differential equations and maps[J]. IEEE Transactions on Circuits and Systems,1988,35(7):850-862.
[4] CHUA L O, KOKUBU H. Normal forms for nonlinear vector fields. I. Theory and algorithm[J]. IEEE Transactions on Circuits and Systems,1988,35(7):863-880.
[5] CHUA L O, KOKUBU H. Normal forms for nonlinear vector fields. II. Applications[J]. IEEE Transactions on Circuits and Systems,1989,36(1):51-70.
[6] WIGGINS S. Introduction to Applied Nonlinear Dynamical Systems and Chaos[M]. New York: SpringerVerlag,1990:211-239.
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[8] YUAN Y, YU P. Computation of simplest normal forms of differential equations associated with a doublezero eigenvalue[J]. International Journal of Bifurcation and Chaos,2001,11(5):1307-1330.
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相似文献/References:

[1]李梦晓,黄土森.一类广义鞍结平面系统正规形的计算[J].浙江理工大学学报,2017,37-38(自科1):116.
 LI Mengxiao,HUANG Tusen.Computation of Normal Forms for a Type of Generalized Planar Saddlenode System[J].Journal of Zhejiang Sci-Tech University,2017,37-38(自科6):116.
[2]刘燕,黄土森.解析系统初等奇点逆积分因子的存在性[J].浙江理工大学学报,2017,37-38(自科4):557.
 LIU Yan,HUANG Tusen.Existence of Inverse Integrating Factors at Elementary Singular Point[J].Journal of Zhejiang Sci-Tech University,2017,37-38(自科6):557.

备注/Memo

备注/Memo:
收稿日期: 2017-03-21
网络出版日期: 2017-05-24
基金项目: 国家自然科学基金项目(11671359,11672270)
作者简介: 张晶(1992-),女,安徽涡阳人,硕士研究生,主要从事微分方程与动力系统方面的研究
更新日期/Last Update: 2017-11-16