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

共 50 条

[41] Polynomial differential systems with hyperbolic algebraic limit cycles
Benyoucef, Salah
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2020, (34) : 1 - 7
[42] On vector fields with prescribed limit cycles
Korchagin A.B.
Qualitative Theory of Dynamical Systems, 2005, 6 (2) : 217 - 232
[43] Non algebraic limit cycles for family of autonomous polynomial planar differential systems
Bendjeddou, A.
Kina, A.
PUNJAB UNIVERSITY JOURNAL OF MATHEMATICS, 2019, 51 (10): : 57 - 63
[44] On the existence of non-hyperbolic ergodic measures as the limit of periodic measures
Bonatti, Christian
Zhang, Jinhua
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2019, 39 : 2932 - 2967
[45] CONFIGURATIONS OF FANS AND NESTS OF LIMIT-CYCLES FOR POLYNOMIAL VECTOR-FIELDS IN THE PLANE
CIMA, A
LLIBRE, J
JOURNAL OF DIFFERENTIAL EQUATIONS, 1989, 82 (01) : 71 - 97
[46] Non-algebraic invariant curves for polynomial planar vector fields
García, IA
Giné, J
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2004, 10 (03) : 755 - 768
[47] On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields
Lubomir Gavrilov
Functional Analysis and Its Applications, 2013, 47 : 174 - 186
[48] On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields
Gavrilov, Lubomir
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2013, 47 (03) : 174 - 186
[49] On the limit cycles of a quintic planar vector field
Yu-hai Wu
Li-xin Tian
Mao-an Han
Science in China Series A: Mathematics, 2007, 50 : 925 - 940
[50] On the limit cycles of a quintic planar vector field
Wu, Yu-hai
Tian, Li-xin
Han, Mao-an
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2007, 50 (07): : 925 - 940

← 1 2 3 4 5 →