一类受摄保测度映射的性态

BEHAVIOUR OF A CLASS OF PERTURBED MEASUREPRESERVING MAPPINGS

我们讨论了一类具有抛物不动点的二维保面积映射的一种受摄扩张:T_3:()? X_(n+1)=X_n-Ay_2~3+B sin z_n,y_(n+1)=x_n+y_n-Ay_n^3+C sin x_n+1,z_n+1=z_n+D sin y_(n+1)+E(mod 2π),其中A、B、C、D、E 为参数。我们发现了一些有趣的性态,有的与文[3],[5]中的结果相似。我们还发现了一些特殊的性态:当 B=C=D=0.03,E=0.009时,仅在围绕原点的环域中产生二维不变流形(不变管子)。当摄动参数 B、C、D、E 减小时,相应的环域扩大了,即在受摄扩张下接近抛物不动点的有序区要比离不动点运的环域内的有序区更容易受到破坏。

We discuss the perturbed extension of an area-preserving mappings with the parabolic fixed point T_3 x_(n+1)=x_n-Ay_n^3+B sin z_n,y_(n+1)=x_n+y_n-Ay_n^3+C sin x_(n+1),z_(n+1)=z_n+D sin y_(n+1)+E,(mod 2π) where A,B,C,D,E,are parameters.We find some interesting results,some of which are similar to those in[3]、[5]. We find also some now behaviours as follows:for B=C=D=0.03,E= 0.009,the two-dimensienal invariant manifolds(invariant tubes)can only be generated in an annulus surrounding the origin,when the perturbation para- meters B,C,D,E,decrease,the area of corresponding annulus increases, i,e.the ordered region near the parabolic fixed point is destroyed by the pe- rturbed extension more easily than the one in an annulus distant from it