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The Closed Orbits of a Class of Cubic Vector Fields in R~3

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成果类型:
期刊论文
作者:
Yin, Hong Yan;Zhou, Da;Zhang, Xing An*
通讯作者:
Zhang, Xing An
作者机构:
[Zhang, Xing An; Yin, Hong Yan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
[Yin, Hong Yan] South Cent Univ Nationalities, Sch Math & Stat, Wuhan 430074, Peoples R China.
[Zhou, Da] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.
通讯机构:
[Zhang, Xing An] C
Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
语种:
英文
关键词:
Closed orbit;central projection transformation;tangent vector field;invariant cone
期刊:
数学学报:英文版
ISSN:
1439-8516
年:
2020
卷:
36
期:
12
页码:
1429-1440
基金类别:
National Nature Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11871238, 11971405]; selfdetermined research funds of CCNU from the collegesbasic research and operation of MOE [CCNU16JCZX10]; Natural Science Foundation of Fujian Province of ChinaNatural Science Foundation of Fujian Province [2015J05016]; Fundamental Research Funds of the South-Central University for Nationalities [CZQ13016]
机构署名:
本校为第一且通讯机构
院系归属:
数学与统计学学院
摘要:
In this paper, we investigate the isolated closed orbits of two types of cubic vector fields in Double-struck capital R-3 by using the idea of central projection transformation, which sets up a bridge connecting the vector field X (x) in Double-struck capital R-3 with the planar vector fields. We have proved that the cubic vector field in Double-struck capital R-3 can have two isolated closed orbits or one closed orbit on the invariant cone. As an application of this result, we have shown that a class of 3-dimensional cubic system has at least 10 isolated closed orbits located on 5 invariant c...

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