Polynomial vector fields with prescribed algebraic limit cycles

被引：20

作者：

Christopher, C ^{[1
]}

机构：

[1] Univ Plymouth, Dept Math & Stat, Plymouth PL4 8AA, Devon, England

来源：

GEOMETRIAE DEDICATA | 2001年 / 88卷 / 1-3期

关键词：

real plane; algebraic curves; Hilbert's 16th problem;

D O I：

10.1023/A:1013171019668

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For each non-singular real algebraic curve f = 0 of degree m we exhibit an explicit vector field of degree m which has precisely the bounded components of f = 0 as limit cycles. The degree of the system is optimal for a generic class of algebraic curves and improves the significantly the bounds given by Winkel.

引用

页码：255 / 258

页数：4

共 10 条

[1]

[Anonymous], 1999, QUAL THEORY DIFF SYS

[2]

Bautin N.N., 1980, DIFF URAVN, V16, P362

[3] THE POINCARE PROBLEM IN THE NONDICRITICAL CASE [J].