第三讲 平面奇点指数

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,第三讲 平面奇点指数,连续向量场的旋转数,平面奇点指标,中心流形,2024/9/21,1,2024/9/21,2,连续向量场的旋转数,2024/9/21,3,2024/9/21,4,2024/9/21,5,旋转数定义,2024/9/21,6,旋转数计算公式,2024/9/21,7,2024/9/21,8,2024/9/21,9,2024/9/21,10,2024/9/21,11,2024/9/21,12,2024/9/21,13,2024/9/21,14,平面奇点指数,2024/9/21,15,2024/9/21,16,2024/9/21,17,2024/9/21,18,2024/9/21,19,2024/9/21,20,2024/9/21,21,2024/9/21,22,2024/9/21,23,2024/9/21,24,2024/9/21,25,2024/9/21,26,2024/9/21,27,2024/9/21,28,2024/9/21,29,2024/9/21,30,性质,2024/9/21,31,推论,2024/9/21,32,平面系统以及二维非自治连续系统 的局部分岔与全局分岔,向量场不动点的分岔,具有一个零特征根,Saddle-node bifurcation,Transcritical bifurcation,Pitchfork bifurcation,一对纯虚根：,Hopf,分岔,2024/9/21,33,向量场不动点的分岔,2024/9/21,34,具有一个零特征根,2024/9/21,35,2024/9/21,36,Transcritical bifurcation,2024/9/21,37,2024/9/21,38,Pitchfork bifurcation,2024/9/21,39,2024/9/21,40,一对纯虚根：,Hopf,分岔,2024/9/21,41,2024/9/21,42,2024/9/21,43,2024/9/21,44,2024/9/21,45,d0,a0,supercritical bifurcation,2024/9/21,46,2024/9/21,47,2024/9/21,48,中心流形,(center manifold),2024/9/21,49,2024/9/21,50,2024/9/21,51,2024/9/21,52,2024/9/21,53,2024/9/21,54,2024/9/21,55,2024/9/21,56,2024/9/21,57,2024/9/21,58,2024/9/21,59,2024/9/21,60,2024/9/21,61,2024/9/21,62,2024/9/21,63,2024/9/21,64,2024/9/21,65,极限点,2024/9/21,66,极限集,2024/9/21,67,吸引集,2024/9/21,68,吸引盆,2024/9/21,69,吸引子,2024/9/21,70,极限集性质,2024/9/21,71,Poincar,-Bendixson,定理,2024/9/21,72,周期解,2024/9/21,73,Thank you very much for your attention,2024/9/21,74,