动态系统中鞍点处的熵与分维

FRACTAL DIMENSION AND ENTROPY BY A SADDLE FIXED POINT IN DYNAMICAL SYSTEMS

若ｆ（ｘ，ｙ）在不动点为鞍点的特征值满足λ１＞１＞｜λ２｜＞０，｜λ１·λ２｜＜１，则ｆ（ｘ，ｙ）限制在鞍点的局部有公式α＝１＋１ｎｒ是局部熵，α是局部分维数．把公式应用到Ｈｅｎｏｎ映射中，当α＝１．４，ｂ＝０．３时，得到１ｎｒ＝０．４５４，α＝１．２４４．

If f(x,y)has a saddle fixed point whose eigenvalue satisfies f(x, y) will have a local formula when it is restricted to a small region around the fixed point, In r is called a local entropy and α a fractal dimension. Applying this formula to the Henon map, at α=1.4, b =0.3, we have ln r = 0.454, α= 1.244.