Limit periodic sets in polynomial liénard equations

被引：0
|
作者：
Luca S. [1 ]
Dumortier F. [1 ]
机构：
[1] Hasselt University, B-3590 Diepenbeek, Campus Diepenbeek, Agoralaan-Gebouw D
来源：
Qualitative Theory of Dynamical Systems | 2009年 / 7卷 / 2期
关键词：
Liénard equation; Limit periodic set; Period annulus; Singularities;
D O I：
10.1007/s12346-008-0019-9
中图分类号：
学科分类号：
摘要：
In this paper we classify all limit periodic sets, as well bounded as unbounded ones, that occur in Liénard equations ẋ = y, ẏ = P(x) + yQ(x), with P and Q polynomials of respective degrees m and n with mn ≥ 1. We also classify the interior and exterior boundaries of the period annuli of such systems with special attention to the exterior boundary of the Hopf centers. We investigate under which conditions on (m, n) certain configurations can occur. © 2008 Birkhäuser Verlag Basel/Switzerland.
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页码：339 / 366
页数：27
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