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| Home > Articles > Published articles > Solution of the Center Problem for a Class of Polynomial Differential Systems |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Date: | 2024 |
| Abstract: | Consider the polynomial differential system of degree m of the form (Formula presented. ) where μ and ν are real numbers such that (μ+ν)(μ+ν(m-2))(a +a )≠0,m>2 and Ω(x,y) is a homogenous polynomial of degree m - 1. A conjecture, stated in J. Differential Equations 2019, suggests that when ν = 1, this differential system has a weak center at the origin if and only if after a convenient linear change of variable (x,y) → (X,Y) the system is invariant under the transformation (X,Y,t) → (-X,Y, -t). For every degree m we prove the extension of this conjecture to any value of ν except for a finite set of values of μ. |
| Grants: | Agencia Estatal de Investigación MTM2016-77278-P Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911 |
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| Language: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Subject: | Center problem ; Polynomial differential system |
| Published in: | Acta Mathematica Sinica. English Series, Vol. 40, Issue 7 (July 2024) , p. 1685-1696, ISSN 1439-7617 |
12 p, 783.6 KB |
