| 摘要: |
| Fix a collection of polynomial vector fields on R3 with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue.Some such systems admit a local analytic first integral,which then defines a local center manifold of the system.Conditions for existence of a first integral are given by the vanishing certain polynomial or rational functions in the coefficients of the system called focus quantities.In this paper we prove that the focus quantities have a structure analogous to that in the two-dimensional case and use it to formulate an efficient algorithm for computing them. |
| 关键词: Integrability center conditions focus quantities |
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| 基金项目:the Slovenian Research Agency and by a Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme,FP7-PEOPLE-2012-IRSES-316338 |
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| Computation of focus quantities of three-dimensional polynomial systems |
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