ON THE DECISION PROBLEM OF THE CENTER OR FOCUS FOR A CLASS OF PLANAR POLYNOMIAL FIELDS

ON THE DECISION PROBLEM OF THE CENTER OR FOCUS FOR A CLASS OF PLANAR POLYNOMIAL FIELDS *

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摘要 In this paper we study the decision problem of the center or focus for a class of planar polynomial fields which can be changed into Abel equation. Taking a Poincaré return map h(x) , we can calculate any order derivative of h(x) at x=0 and obtain the focus value of each order. The new method in this paper avoids the recurence operation and reduces the work in calculating the focus value. In this paper we study the decision problem of the center or focus for a class of planar polynomial fields which can be changed into Abel equation. Taking a Poincaré return map h(x) , we can calculate any order derivative of h(x) at x=0 and obtain the focus value of each order. The new method in this paper avoids the recurence operation and reduces the work in calculating the focus value.

作者谢向东蔡燧林

机构地区宁德师专浙江大学

出处《Annals of Differential Equations》 1998年第1期81-90,共10页 微分方程年刊（英文版）

关键词 decision problem of the center or focus Abel equation Poincaré return map. decision problem of the center or focus, Abel equation, Poincaré return map.

分类号 O175.24 [理学—基础数学]

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Annals of Differential Equations

1998年第1期

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ON THE DECISION PROBLEM OF THE CENTER OR FOCUS FOR A CLASS OF PLANAR POLYNOMIAL FIELDS

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