Computation of focus quantities of three-dimensional polynomial systems
Fix a collection of polynomial vector fields on <i>R</i><sup>3</sup> 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 def...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Academic Journals Center of Shanghai Normal University
2014-10-01
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| Series: | Journal of Shanghai Normal University (Natural Sciences) |
| Subjects: | |
| Online Access: | http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/create_pdf.aspx?file_no=201405010&flag=1&year_id=2014&quarter_id=5 |
| Summary: | Fix a collection of polynomial vector fields on <i>R</i><sup>3</sup> 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. |
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| ISSN: | 1000-5137 1000-5137 |