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Uniqueness of Limit Cycles in Polynomial Systems with Algebraic Invariants

机译：具有代数不变量的多项式系统极限环的唯一性

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The uniqueness of limit cycles is proved for quadratic systems with an invariantparabola and for cubic systems with four real line invariants. Also a new, simple proof is given of the uniqueness of limit cycles occurring in unfoldings of certain vector fields with codimension two singularities. (Copyright (c) 1992 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)

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作者
Zegeling, A.; Kooij, R. E.;
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年度 1992
页码 1-24
总页数 24
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Differential equations; Vector fields; Singularity; Polynomials; Uniqueness theorem;

机译：微分方程;向量场;奇异性;多项式;唯一性定理;

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2. Invariant Parallels, Invariant Meridians and Limit Cycles of Polynomial Vector Fields on Some 2-Dimensional Algebraic Tori in R~3 [J] . Jaume Llibre, Salomon Rebollo-Perdomo Journal of dynamics and differential equations . 2013,第3期

机译：R〜3中某些二维代数环上的多项式矢量场的不变平行，不变子午线和极限环
3. Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields [J] . Garcia IA The Rocky Mountain journal of mathematics . 2005,第2期

机译：通过多项式平面矢量场的任意度不变代数曲线的结构实现超越极限环
4. Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems [C] . Wei Niu, Dongming Wang Algebraic Biology . 2008

机译：生物系统分叉和极限环的代数分析
5. On the maximum number of limit cycles of certain polynomial Lienard equations. [D] . Yao, Leummim. 1995

机译：关于某些多项式Lienard方程的极限环的最大数目。
6. Symmetric hyperbolic systems in algebras of generalized functions and distributional limits [O] . Günther Hörmann, Christian Spreitzer -1

机译：广义函数和分布极限的代数中的对称双曲系统
7. On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity [O] . Llibre Jaume 2017

机译：具有无限对两点平衡点的二次多项式微分系统的代数极限环的唯一性
8. Infinite Separatrix Cycles in the Critical Case, Divergence and Uniqueness of Limit Cycles of a Quadratic Differential System [R] . Yanqian, Y. 1989

机译：二次微分系统极限环的临界情形，发散和唯一性中的无穷矩阵循环

Uniqueness of Limit Cycles in Polynomial Systems with Algebraic Invariants

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