单峰扩张映射的捏制序列

设Ｐ及ＡＣ均是准素序列并满足ｍｉｎ｛Ｐ，ＡＣ｝ＲＬＲ∞，ρ（Ｐ）及ρ（ＡＣ）分别是Ｐ及ＡＣ的特征值．设ｆ∈Ｃ０（Ｉ，Ｉ）是个单峰扩张映射并具有扩张常数λ，ｍ是个非负整数．本文证明了若λ（ρ（Ｐ））１／２ｍ，则ｆ的捏制序列Ｋ（ｆ）（ＲＣ）ｍＰ；若λ＞（ρ（ＡＣ））１／２ｍ，则对任极大序列Ｅ，Ｋ（ｆ）＞（ＲＣ）ｍＡＣＥ．（ρ（Ｐ））１／２ｍ及（ρ（ＡＣ））１／２ｍ均是下述意义下的最佳值，即若其中任一个被较小的值代替，则相应的结论便不成立．

Kneading Sequences for Unimodal Expanding Maps of the Interval

Let P and AC be two primary sequences with  min {P,AC}RLR ∞, ρ(P) and ρ(AC) be the eigenvalues of P and AC, respectively. Let f∈C 0(I,I) be a unimodal expanding map with expanding constant λ and m be a nonegative integer. It is proved that f has the kneading sequence K(f)(RC) *m *P if λ(ρ(P)) 1/2 m , and K(f)>(RC) *m * AC*E for any shift maximal sequence E if λ>(ρ(AC)) 1/2 m .The value of (ρ(P)) 1/2 m  or (ρ(AC)) 1/2 m  is the best possible in the sense that the related conclusion may not be true if it is replaced by any smaller one.