On the structural instability of non-hyperbolic limit cycles on planar polynomial vector fields

被引：2

作者：

Santana, Paulo ^{[1
]}

机构：

[1] UNESP, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

来源：

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES | 2024年

基金：

巴西圣保罗研究基金会;

关键词：

Structural stability; Limit cycles; Polynomial vector fields; STABILITY; BIFURCATION;

D O I：

10.1007/s40863-024-00431-w

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is known that non-hyperbolic limit cycles are structurally unstable in the set of planar smooth and analytic vector fields. In the polynomial case, it is known only that limit cycles of even degree are structurally unstable. In this paper, we prove that non-hyperbolic limit cycles of odd degree are also structurally unstable in the polynomial case, if we consider Whitney's topology.

引用

页码：1605 / 1618

页数：14

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