Isochronicity Problem of Higher-Order Singular Point for Polynomial Differential Systems

被引：0
作者：
Yusen Wu
Cui Zhang
Peiluan Li
机构：
[1] Central South University,School of Mathematical Science and Computing Technology
[2] Luoyang Normal University,School of Mathematical Science
来源：
Acta Applicandae Mathematicae | 2010年 / 110卷
关键词：
Higher-order singular point; Period constant; Recursive algorithm; Polynomial differential system; 34C05; 34C07;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Due to the difficulty, the isochronicity problems with respect to higher-order singular point (or degenerate singular point) of polynomial differential systems are far from being solved. The calculation of period constants is an effective way to find necessary conditions for isochronicity. In this paper, by means of a homeomorphic transformation, higher-order singular point is transferred into the origin. At the same time, a new recursive algorithm to compute period constants at the origin of the transformed system is deduced which is easy to realize with the computer algebraic system such as MATHEMATICA or MAPLE. Finally, to illustrate the effectiveness of our algorithm, the pseudo-isochronous center conditions of higher-order singular point for a class of septic system are investigated. Our work is new in terms of research about the isochronicity problem of higher-order singular point and consists of the existing results related to the origin as a special case when it is an elementary singular point.
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页码：1429 / 1448
页数：19
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