INTEGRABILITY OF A LINEAR CENTER PERTURBED BY A FIFTH DEGREE HOMOGENEOUS POLYNOMIAL

被引:49
作者
Chavarriga, Javier [1 ]
Gine, Jaume [1 ]
机构
[1] Univ Lleida, Escola Tecn Super Engn Agr, Avda Alcalde Rovira Roure 177, Lleida 25006, Spain
关键词
Center-focus problem; integrable systems in the plane;
D O I
10.5565/PUBLMAT_41297_02
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.
引用
收藏
页码:335 / 356
页数:22
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