科研之友
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摘要
We consider center conditions for plane polynomial systems of Abel type consisting of a linear center perturbed by the sum of 2 homogeneous polynomials of degrees n and 2n - 1 where n >= 2. Using properties of Abel equations we obtain two general systems valid for arbitrary values on n. For the cubic n - 2 systems we find several sets of new center conditions, some of which show that the results in a paper by Hill, Lloyd and Pearson which were conjectured to be complete are in fact not complete. We also present a particular system which appears to be a counterexample to a conjecture by Zoladek et al. regarding rational reversibility in cubic polynomial systems.
- 出版日期2015-7-16
