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The Poincare center-focus problem for a class of higher order polynomial differential systems

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 نشر من قبل Zhengxin Zhou
 تاريخ النشر 2018
  مجال البحث
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 تأليف Zhengxin Zhou




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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.



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