“倍周期分支通向混沌”的分形变量──计算机辅助数值分析

Fractal Measure of the Route "Period-doubling Leads to Chaos"──Computer-assisted quantitative analysis

本文基于集合分形的定义，对“倍周期分支通向混沌”这一途径的分形度量──分形示性数及分形维数进行数值分析，揭示倍周期分支进入混沌时的分形维数为ｄ_Ｆｄ_Ｆ（Ｘ∞）＝０．５０７０９６８…具有普适性。

Based on the defination of set fractal a quantitative analysis is made towards the route of 'Period-doubling leads to Chaos' by calculecting its fractal measure fractal characteristic number and fractal dimension. It is discovered that the fractal dimension is 0.5 070968…. which is universal when it enters into chaos through Period-doubling.