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2n的正则Fμ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.
By a piecewise linear unimodal map,we described the mathematical of Feigenbaum attractor and proved that the quadratic family possessed a nest of proper Fμ cycles with period 2n 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.
谢建华. Feigenbaum吸引子的结构[J].动力学与控制学报,2003,1(1):9~13; Xie Jianhua. The structure of feigenbaum attractor[J]. Journal of Dynamics and Control,2003,1(1):9-13.
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