Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4669173 | Bulletin des Sciences Mathématiques | 2008 | 13 Pages |
Abstract
By using an effective complex algorithm to calculate the Lyapunov constants of polynomial systems En: zË=iz+Rn(z,z¯), where Rn is a homogeneous polynomial of degree n, in this note we construct two concrete examples, E4 and E5, such that in both cases, the corresponding orders of fine focus can be as high as 18. The systems are given, respectively, by the following ordinary differential equations:E4:zË=iz+2iz4+izz¯3+5227820723eiθz¯4, where θâ{kϱÏ6,kÏ+Ï2,kâZ}, andE5:zË=iz+3z5+20(c+3)9c2â15z4z¯+zz¯4+20(c+3)c29c2â15z¯5, where c is the root between (â3,â5/3) of the equation4155c6â10716c5â63285c4â18070c3+168075c2+205450c+60375=0.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jing Huang, Fang Wang, Lu Wang, Jiazhong Yang,