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| Solution of Center-Focus Problem for a Class of Cubic Systems |
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Citation： |
Bo SANG,Chuanze NIU.Solution of Center-Focus Problem for a Class of Cubic Systems[J].Chinese Annals of Mathematics B,2016,37(1):149~160 |
| Page view： 3685
Net amount： 1447 |
Authors： |
Bo SANG; Chuanze NIU |
Foundation： |
This work was supported by
the National Natural Science Foundation of China (No.\,11401285) and
the Foundation for Research in Experimental Techniques of Liaocheng University
(No.\,LDSY2014110). |
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| Abstract： |
For a class of cubic systems, the authors give a representation of
the $n${\rm th} order Liapunov constant through a chain of
pseudo-divisions. As an application, the center problem and the
isochronous center problem of a particular system are considered.
They show that the system has a center at the origin if and only if
the first seven Liapunov constants vanish, and cannot have an
isochronous center at the origin. |
Keywords： |
Center variety, Isochronous center, Center conditions,
Integrating factor |
Classification： |
34C05, 34C07 |
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