科研之友
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摘要
We mainly investigate the likely limit sets and the kneading sequences of unimodal Feigenbaum's maps (Feigenbaum's map can be regarded as the fixed point of the renormalization operator T : f bar right arrow lambda(-1) f(2)lambda, where lambda is to be determined). First, we estimate the Hausdorff dimension of the likely limit set for the unimodal Feigenbaum's map and then for every decimal s is an element of (0, 1), we construct a unimodal Feigenbaum's map which has a likely limit set with Hausdorff dimensions. Second, we prove that the kneading sequences of unimodal Feigenbaum's maps are uniformly almost periodic points of the shift map but not periodic ones.
