赤道环

本文研究一类形式相当一般的平面多项式系统赤道环量（Gauss球面的无穷远点奇点量）的计算，建立了系统赤道环量计算的简明的线性代数递推公式。

In this paper , we study the computation of quantities of equator ( singular point quantities of infinity at Gauss sphere ) in a class of planar polynomial differential system with a general form . Two linear recursion formulas for computation of quantities of equator are obtained .

一类五次系统赤道环的稳定性与极限环分枝

Stability and limit cycle bifurcation of equator for a class of fifth system

该系统的原点是高次奇点，赤道环上没有实奇点。

In the system , the origin is degenerate critical point and the equator contains no real critical point .

但在成形过程中，壳体赤道环焊缝处极易向内收缩，从而引发该处的失稳起皱，严重影响了球形容器的质量。

But in the forming process , equator of the shell tends to withdraw inwards and therefore creates wrinkles here , which badly affects the quality of the vessel .

另一个是直立在赤道环中心的双环，能绕一根金属轴转动，叫做“赤经双环”。

and the other is a double-ring which is per-pendicular to the center of the equatorial ring ， revolving around a metallic shaft ， and is called " right ascension double-ring .

观测时，将窥管对准某颗待测星，然后在赤道环和赤经双环的刻度盘上直接读出这颗星星的位置值。

During observation ， the sighting tube is targeted at a certain star , thus the positional value can be read out at the dials of the equatorial ring and the right ascension double-ring .

将这类实三次系统转化为复平面系统研究，给出了系统赤道环量的易于计算的线性代数递推公式。一类奇数次多项式系统赤道环的稳定性

By translating this real cubic system into a complex planar system , an applicable linear algebraic recursion formula of the equator and the first 6 quantities of the equator are given . Stability of Equator for a Class of Odd Number Degree Polynomial System

在赤经环面上装着一根望筒，可以绕赤经环中心转动，用望筒对准某颗星星，然后，根据赤道环和赤经环上的刻度来确定该星在天空中的位置。

An observatory tube was fixed on the Chijing ring and could rotate around the center of the ring . When used for examining the position of stars ， the tube was first aimed at a certain star ; then the graduation on the equator and Chijing rings was used to pin-point the star 's position in the sky .

对各种变化时空特征的分析表明：①Dst变化清楚地反映出赤道对称环电流磁扰的空间分布和时间演化特征；

The results show that the spacial distribution and the temporal evolution characteristic of equatorial symmetric ring current are reflected clearly by Dst variation .

一类平面三次多项式系统的赤道极限环分支

Bifurcation of limit cycles of the equator in a class of cubic polynomial system

本论文研究平面多项式微分系统的中心焦点判定与赤道极限环分支，由七章组成。

This thesis is devoted to qualitative analysis for some planar polynomial differential autonomous systems .

在第一章，我们对平面多项式微分系统的中心焦点判定与赤道极限环分支问题研究的历史背景与现状进行了全面综述。

In Chapter 1 , the background and present conditions are introduced and summarized for the study of center-focus determination and bifurcation of limit cycles of the equator for planar polynomial differential systems .

环球赤道Ω涡环拟序结构

The Ω Vortex Sequencing Structure Around the Global Equator

最外面的那个圆环固定在正南北方向上，叫做“子午环”；中间固定着的圆环平行于地球赤道面，叫做“赤道环”；最里面的圆环可以绕金属轴旋转，叫做“赤经环”；

The outermost ring-meridian ring-was fixed in the north-south direction ， the middle ring-equator ring-was parallel to the earth 's e-quatorial plane ， and the innermost one-Chijing ring-could revolve around the metal axis .

简仪的主要装置是由两个互相垂直的大圆环组成，其中的一个环面平行于地球赤道面，叫做“赤道环”；

The primary structure of Abridged Armilla contains two large rings that are per-pendicular to each other , of which one is parallel with the equatorial plane and is accordingly called " equatorial ring ; ，

在第三章至第六章，我们研究实平面奇数次多项式微分系统无穷远点（赤道）的中心焦点判定与赤道极限环分支。

From Chapter 3 to Chapter 6 , the center-focus determination and bifurcation of the equator are studied for real planar odd polynomial differential systems .