函数的H-导数和分形动力学

 给出了函数的Hausdorff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，给出了分形动力学的演化方程组并做了初步讨论与分析。

H DERIVATIVE OF THE FUNCTION AND THE FRACTAL DYNAMICS

In this paper, Hausdorff measure of the function f(x) and H-derivative of the function f(x) under Hausdorff measure are given as follows: H^Df(x)]= sup_n{∑ⁿ_j=1|f(x_j)-f(x_j-1)|^D} and f⁽¹⁾_H(x,0)=lim_Δx→0|f(x₀+ Δx)-f(x₀+ Δx)|^D]/(2Δx)^D=|f(x₀)|^D. The system of evolution equation of fractal dynamics is u⁽¹⁾_Ht=k(x)u⁽²⁾_Hxx-αu⁽¹⁾_Hx, dD/dt=f(p₁, p₂), where the first equation is called the equation of fractal dynamics, and the second equation is called the evolution equation of Hausdorff dimension D.