The Poincaré center‐focus problem for a class of higher order polynomial differential systems
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Publication:5380774
DOI10.1002/MMA.5475zbMATH Open1458.34064arXiv1811.11893OpenAlexW2902294101MaRDI QIDQ5380774
Publication date: 6 June 2019
Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)
Abstract: In this paper, I have proved that for a class of polynomial differential systems of degree n+1 ( where n is an arbitrary positive integer) the composition conjecture is true. I give the sufficient and necessary conditions for these differential systems to have a center at origin point by using a different method from the previous references. By this I can obtain all the focal values of these systems for an arbitrary n and their expressions are succinct and beautiful. I believe that the idea and method of this article can be used to solve the center-focus problem of more high-order polynomial differential systems.
Full work available at URL: https://arxiv.org/abs/1811.11893
Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)
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