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A quartic system and a quintic system with fine focus of order 18
- Source :
- Bulletin des Sciences Mathématiques. (3):205-217
- Publisher :
- Elsevier Masson SAS.
-
Abstract
- By using an effective complex algorithm to calculate the Lyapunov constants of polynomial systems En: z˙=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:z˙=iz+2iz4+izz¯3+5227820723eiθz¯4, where θ∉{kπ±π6,kπ+π2,k∈Z}, and E5:z˙=iz+3z5+20(c+3)9c2−15z4z¯+zz¯4+20(c+3)c29c2−15z¯5, where c is the root between (−3,−5/3) of the equation 4155c6−10716c5−63285c4−18070c3+168075c2+205450c+60375=0.
- Subjects :
- Polynomial
Mathematics(all)
Lyapunov constants
Differential equation
General Mathematics
Center (category theory)
Geometry
Center–focus
Quintic function
Homogeneous polynomial
Ordinary differential equation
Quartic function
Order (group theory)
Quintic systems
Quartic systems
Fine focus
Mathematics
Mathematical physics
Subjects
Details
- Language :
- English
- ISSN :
- 00074497
- Issue :
- 3
- Database :
- OpenAIRE
- Journal :
- Bulletin des Sciences Mathématiques
- Accession number :
- edsair.doi.dedup.....c9851cf4cf17c839101808acf9e0a6d4
- Full Text :
- https://doi.org/10.1016/j.bulsci.2006.12.006