Planar Quadratic Vector Fields with Two or Three Finite Singularities and a Finite Saddle Connection on a Straight Line

P. C. Carri?o; M. E. S. Gomes; A. A. G. Ruas

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Planar Quadratic Vector Fields with Two or Three Finite Singularities and a Finite Saddle Connection on a Straight Line

机译：具有两个或三个有限奇点和一条直线上的有限鞍形连接的平面二次矢量场

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摘要

We classify the phase portraits of planar quadratic vector fields with a invariant straight line passing through two finite saddles, when the vector field has two or three finite singularities.

机译：当矢量场具有两个或三个有限奇点时，我们用经过两个有限鞍的不变直线对平面二次矢量场的相图进行分类。

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来源
《Qualitative Theory of Dynamical Systems》 |2009年第1期|25-44|共20页
作者
P. C. Carri?o; M. E. S. Gomes; A. A. G. Ruas;
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作者单位

Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, 30123-970, MG, Brazil;

Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, 30123-970, MG, Brazil;

Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, 30123-970, MG, Brazil;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Quadratic vector field; Saddle connection;

机译：二次向量场;鞍座连接;

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专利

1. Planar Quadratic Vector Fields with Two or Three Finite Singularities and a Finite Saddle Connection on a Straight Line [J] . P. C. Carriao, M. E. S. Gomes, A. A. G. Ruas Qualitative theory of dynamical systems . 2009,第1期

机译：具有两个或三个有限奇点和一条直线上的有限鞍形连接的平面二次矢量场
2. Planar Quadratic Vector Fields with Finite Saddle Connection on a Straight Line (Non-convex Case) [J] . Paulo César Carri?o, Maria Elasir Seabra Gomes, Antonio Augusto Gaspar Ruas Qualitative Theory of Dynamical Systems . 2009,第2期

机译：在直线上具有有限鞍形连接的平面二次矢量场（非凸案例）
3. Bifurcation Diagrams and Moduli Spaces of Planar Quadratic Vector Fields with Invariant Lines of Total Multiplicity Four and Having Exactly Three Real Singularities at Infinity [J] . Dana Schlomiuk, Nicolae Vulpe Qualitative theory of dynamical systems . 2010,第1a2期

机译：平面二次向量场的分叉图和模空间，其中不变线的总重数为4，且无穷大的实奇点为3
4. Normal Forms for Germs of Analytic Families of Planar Vector Fields Unfolding a Generic Saddle-node or Resonant Saddle [C] . Christiane Rousseau International Conference on Nonlinear Dynamics and Evolution Equations . 2006

机译：平面矢量场的分析家族细菌正常形式展开通用鞍座节点或谐振鞍座
5. Finite point configurations and projection theorems in vector spaces over finite fields [D] . Chapman, Jeremy 2010

机译：有限域上向量空间中的有限点配置和投影定理
6. On Cyclotomy and Extensions of Gaussian Type Quadratic Relations Involving Numbers of Solutions of Conditional Equations in Finite Fields [O] . H. S. Vandiver 1952

机译：关于有限域中条件方程解数的高斯型二次关系的切线和扩展
7. Notes on Finitely Determined Singularities of Formal Vector Fields (Singularities of Differentiable Mappings) [O] . ICHIKAWA FUMIO 1980

机译：关于形式矢量场的有限确定奇点（可微映射的奇点）的注释
8. There Is No Finite Classification for Homogeneous Quadratic Vector Fields on R Cubed, Moduli of Stability [R] . Vanstrien, S. J., Tavaresdossantos, G. 1985

机译：R Cubed，稳定模量上的齐次二次矢量场没有有限分类

Planar Quadratic Vector Fields with Two or Three Finite Singularities and a Finite Saddle Connection on a Straight Line

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