Gary R. Nicklason
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 . 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.
Submitted March 30, 2015. Published July 16, 2015.
Math Subject Classifications: 34A05, 34C25.
Key Words: Center-focus problem; Abel differential equation; constant invariant; symmetric centers.
Show me the PDF file (258 KB), TEX file, and other files for this article.
| Gary R. Nicklason |
Mathematics, Physics and Geology
Cape Breton University
Sydney, Nova Scotia, B1P 6L2, Canada
Return to the EJDE web page