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On the limit cycles of polynomial differential systems with homogeneous nonlinearities

Published online by Cambridge University Press:  20 January 2009

Chengzhi Li ,
Weigu Li ,
Jaume Llibre  and
Zhifen Zhang
Chengzhi Li
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, People's Republic of China
Weigu Li
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, People's Republic of China
Jaume Llibre
Affiliation:
Department de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
Zhifen Zhang
Affiliation:
Department of Mathematics, Peking University, Beijing 100871, People's Republic of China
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Abstract

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We consider three classes of polynomial differential equations of the form ẋ = y + establish Pn (x, y), ẏ = x + Qn (x, y), where establish Pn and Qn are homogeneous polynomials of degree n, having a non-Hamiltonian centre at the origin. By using a method different from the classical ones, we study the limit cycles that bifurcate from the periodic orbits of such centres when we perturb them inside the class of all polynomial differential systems of the above form. A more detailed study is made for the particular cases of degree n = 2 and n = 3.

Keywords

limit cyclescentresbifurcation
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 3 , October 2000 , pp. 529 - 543
Copyright
Copyright © Edinburgh Mathematical Society 2000

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