Polynomial differential systems with even degree have no global centers

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:503

Article

Llibre, Jaume¹  Valls, Claudia² 

[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Spain

[2] Univ Lisbon, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon, Portugal

关键词: Global centers;    Polynomial differential system;    Poincare compactification;   

DOI  :  10.1016/j.jmaa.2021.125281

来源: Elsevier

【 摘 要 】

Let (x) over dot = P(x, y), (y) over dot = Q(x, y) be a differential system with Pand Qreal polynomials, and let d = max{deg P, deg Q}. A singular point pof this differential system is a global center if R-2\{p} is filled with periodic orbits. We prove that if dis even then the polynomial differential systems have no global centers. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free