【摘要】 用一个分段线性单峰映射描述了二次映射 Feigenbaum 吸引子的数学结构.证明了存在一个周期2~M 的正则 F_μ-圈嵌套序列,由其生成的吸引的极小 Cantor 集与单边符号空间的一个所谓“加法器”拓扑共轭.对现有结果作了若干补充和简化证明.更多还原

【Abstract】 By a piecewise linear unimodal map,we described the mathematical structure of Feigenbaum attractor and proved that the quadratic family possessed a nest of proper F_μ-cycles with period 2~n which determined an attractive minimal Cantor set.The subsystem of the map on the set was topologically conjugate to a so-called“adding machine”on the symbol sequence space.Some supplements were added to the recent results and several proofs were simplified.更多还原