Kneading Sequences for Unimodal Expanding Maps of the Interval

<正> Let P and AC be two primary sequences with min{P, AC} RLR∞,ρ（P） and p（AC）be the eigenvalues of P and AC, respectively. Let f ∈ C0（I, I） be a unimodal expanding map withexpanding constant λ and m be a nonegative integer. It is proved that f has the kneading sequenceK（f） （RC）*m * P i...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 14; no. 4; pp. 457 - 462
Main Author Fanping, Zeng
Format Journal Article
LanguageEnglish
Published Beijing Springer Nature B.V 01.10.1998
Subjects
Eigenvalues
entropy
Integers
Intervals
Mapping
Periodic
point;Kneading
sequence;Topological
Sequences
Studies
Theorems
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Summary:<正> Let P and AC be two primary sequences with min{P, AC} RLR∞,ρ（P） and p（AC）be the eigenvalues of P and AC, respectively. Let f ∈ C0（I, I） be a unimodal expanding map withexpanding constant λ and m be a nonegative integer. It is proved that f has the kneading sequenceK（f） （RC）*m * P if λ （ρ（P））1/2m, and K（f）>（RC）*m * AC * E for any shift maximalsequence E if λ>（ρ（AC））1/2m. The value of （ρ（P））1/2m or （ρ（AC））1/2m is the best possible inthe sense that the related conclusion may not be true if it is replaced by any smaller one.
Bibliography:Let P and AC be two primary sequences with min{P, AC} RLR∞,ρ（P） and p（AC） be the eigenvalues of P and AC, respectively. Let f ∈ C0（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））1/2m, and K（f）>（RC）*m * AC * E for any shift maximal sequence E if λ>（ρ（AC））1/2m. The value of （ρ（P））1/2m or （ρ（AC））1/2m is the best possible in the sense that the related conclusion may not be true if it is replaced by any smaller one.
11-2039/O1
Periodic point;Kneading sequence;Topological entropy
Zeng Fanping, Institute of Mathematics, Guangxi University, Nanning 530004, China
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/BF02580402