英语翻译Note:If you wish your class to sketch trajectories for a

英语翻译
Note:If you wish your class to sketch trajectories for anything except saddle points,you will need to go beyond the discussion in the next.The following remarks from the Study Guide are relevant.
Sketching trajectories for a dynamical system in which the origin is an attractor or a repellor is more difficult than the sketch in Exercise 7.There has been no discussion of the direction in which the trajectories “bend” as they move toward or away from the origin.For instance,if you rotate Figure 1 of Section 5.6 through a quarter-turn and relabel the axes so that x1 is on the horizontal axis,then the new figure corresponds to the matrix A with the diagonal entries .8 and .64 interchanged.In general ,if A is a diagonal matrix,with positive diagonal entries a and d,unequal to 1,then the trajectories lie on the axes or on curves whose equations have the form x2 =r(x1) ,where s=(Ind)/(Ina) and r depends on the initial point x0.(See Encounters with Chaos ,by Denny Gulick,New York:McGraw-Hill,1992,pp.147-150)
8.The matrix from Exercise 2 has eigenvalues 3,4/5 ,and 3/5.Since one eigenvalue is greatest than 1 and the others are less than one in magnitude ,the origin is a saddle point .The direction of greatest repulsion is the line through the origin and the eigenvector (1,0,-3) for the eigenvalue 3 .The direction of greatest attraction is the line through the origin and the eigenvector (-3,-3,7) for the smallest eigenvalue 3/5 .

注意:如果你愿你的班级除了鞍点以外为任何事描绘略图轨道,你将会需要在下一个中超越讨论.来自研究引导者的下列的评论是有关的.
为一个动态的系统草图轨道在一个引起注意的人或者 repellor 是哪起源比练习 7 的素描更困难.已经没有方向的讨论在哪一个轨道 " 弯曲 " 当他们移动向或远离起源.举例来说,如果你整四分之一替换第 5.6 节的图 1-旋转而且再分类轴以便 x 1 在水平的轴上,那么新的身材用对角线的进入符合点阵式一.8 和.64 交换.大体上 ,如果一是一个对角线的点阵式,藉由积极的对角线的进入一和 d,不相等的到 1,那么轨道躺在轴上或者相等有形式 x 2= r(x 1) 的曲线 ,哪里 s=(Ind)/(Ina)和 r 仰赖开始的点 x 0.(用大混乱见到相会 ,由丹尼 Gulick,纽约:McGraw-希尔,1992,pp.147-150)
8.来自练习 2 的点阵式有本征值 3,4/5,和 3/5.因为一个本征值最好超过 1 和其余者是较少的超过一在大小方面,起源是鞍点.最好的击退的方向对于本征值 3 经过起源和 eigenvector(1,0,-3) 是线.最好的吸引的方向对于最小的本征值 3/5 经过起源和 eigenvector(-3,-3,7) 是线.