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[1]贾鲁昆,程金发*,温泳铭.一个庞卡莱映射的逼近[J].厦门大学学报(自然科学版),2017,56(03):384-390.[doi:10.6043/j.issn.0438-0479.201607013]
 JIA Lukun,CHENG Jinfa*,WEN Yongming.Approximations of a Poincaré Map[J].Journal of Xiamen University(Natural Science),2017,56(03):384-390.[doi:10.6043/j.issn.0438-0479.201607013]
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
56卷
期数:
2017年03期
页码:
384-390
栏目:
研究论文
出版日期:
2017-05-24

文章信息/Info

Title:
Approximations of a Poincaré Map
文章编号:
0438-0479(2017)03-0384-07
作者:
贾鲁昆程金发*温泳铭
厦门大学数学科学学院,福建厦门361005
Author(s):
JIA LukunCHENG Jinfa*WEN Yongming
School of Mathematical Sciences,Xiamen University,Xiamen 361005,China
关键词:
庞卡莱映射同宿轨一致逼近
Keywords:
Poincaré maphomoclinic orbitlinearly approximated
分类号:
O 193; O 175.12
DOI:
10.6043/j.issn.0438-0479.201607013
文献标志码:
A
摘要:
在连接同宿轨的双曲不动点附近可以构造一个庞卡莱映射,但一般来说,该庞卡莱映射及其线性逼近在其整个定义域内无法做到一致逼近.通过一个例子说明Wiggins S证明中的一个错误,给出庞卡莱映射在整个定义域内能被逼近的一个充分条件,并证明在庞卡莱映射定义域的一个子集内,该映射与其线性化映射可以做到一致逼近.
Abstract:
We can construct a Poincaré map near a hyperbolic point which joins a homoclinic orbit.But in general,it cannot be uniformly approximated linearly in its whole domain.In this paper,we first show a claim in Stephen Wiggins′ proof is wrong by an example,and then give a sufficient condition under which the Poincaré map can be approximated linearly in its whole domain.In the end,using our method we get a subset in which the Poincaré map can be linearly approximated.

参考文献/References:

[1] WIGGINS S.Global bifurcations and chaos:analytical methods.Applied mathematical sciences[M].New York:Springer-Verlag,1988:193,196.
[2] HIRSCH M W,PUGH C C,SHUB M.Invariant manifolds.Springer lecture notes in mathematics[M].Berlin,New York:Springer-Verlag,1977:39-52.
[3] BAKALEINIKOV L A,SILBERGLEIT A S.On the applicability of the approximate Poincaré mapping to the analysis of dynamics induced by ODE systems Ⅰ.Proximity of mappings[J].Physica D:Nonlinear Phenomena,1995,83(4):326-341.
[4] 温泳铭,张霞娟,胡建钧,等.关于庞卡莱映射逼近的一个反例[J].厦门大学学报(自然科学版),2015,54(3):369-371.
[5] BAKALEINIKOV L A,SILBERGLEIT A S.On the applicability of the approximate Poincaré mapping to the analysis of dynamics induced by ODE systems Ⅱ.Proximity of coordinate partial derivatives of Poincaré mappings[J].Physica D:Nonlinear Phenomena,1995,83(4):342-354.
[6] HIRSCH M W,SMALLE S,DEVANEY R L.Differential equations,dynamical systems,and an introduction to chaos[M].3rd et.Amsterdam:Elsevier/Academic Press,2004:102.

备注/Memo

备注/Memo:
收稿日期:2016-07-12 录用日期:2016-12-19
基金项目:国家自然科学基金(11401556,11471304); 中央高校青年创新基金(WK2040000012)
*通信作者:jfcheng@xmu.edu.cn
引文格式:贾鲁昆,程金发,温泳铭.一个庞卡莱映射的逼近[J].厦门大学学报(自然科学版),2017,56(3):384-390.
Citation:JIA L K,CHENG J F,WEN Y M.Approximations of a Poincaré map[J].J Xiamen Univ Nat Sci,2017,56(3):384-390.(in Chinese)
更新日期/Last Update: 1900-01-01