摘要
给出了函数的Ｈａｕｓｄｏｒｆ测度与Ｈ－导数。从而，为开展自给的分形动力学提供了解析的数学工具。同时。
In this paper,Hausdorff measure of the function f(x) and H derivative of the function f(x) under Hausdorff measure are given as followsH D= sup n∑nj=1|f(x j)-f(x j-1 )| Dandf (1) H(x 0)= lim Δx→0|f(x 0+ Δ x)-f(x 0- Δ x)| D(2 Δ x) D=|f(x 0)| D The system of evolution equation of fractal dynamics isu (1) Ht =k(x)u (2) Hxx -αu (1) Hx d D/ d t=f(p 1,p 2)where the first equation is called the equation of fractal dynamics,and the second equation is called the evolution equation of Hausdorff dimention D .
出处
《高压物理学报》
CAS
CSCD
北大核心
1997年第1期13-20,共8页
Chinese Journal of High Pressure Physics
基金
国家自然科学基金
关键词
H-导数
演化方程组
分形动力学
Hausdorff measure of the function, H derivative,the system of evolution equation.
