Self-similar structure on the intersection of middle-(1 - 2β) Cantor sets with β ∈ (1/3, 1/2)

Yuru Zou; Jian Lu; Wenxia Li

doi:10.1088/0951-7715/21/12/010

Self-similar structure on the intersection of middle-(1 - 2β) Cantor sets with β ∈ (1/3, 1/2)

Yuru Zou^*
, Jian Lu
, Wenxia Li

^*此作品的通讯作者

数学科学学院

Shenzhen University

科研成果: 期刊稿件 › 文章 › 同行评审

14 引用（Scopus）

摘要

Let Γ_β be the middle-(1 - 2β) Cantor set with β ∈ (1/3, 1/2). We give all real numbers t with unique {-1, 0, 1}-code such that the intersections Γ_β ∩ (Γ _β+t) are self-similar sets. For a given β ∈ (1/3, 1/2), a criterion is obtained to check whether or not a t ∈ [-1, 1] has the unique {-1, 0, 1}-code from both geometric and algebraic views.

源语言	英语
页（从-至）	2899-2910
页数	12
期刊	Nonlinearity
卷	21
期	12
DOI	https://doi.org/10.1088/0951-7715/21/12/010
出版状态	已出版 - 1 12月 2008

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10.1088/0951-7715/21/12/010

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abstract = "Let Γβ be the middle-(1 - 2β) Cantor set with β ∈ (1/3, 1/2). We give all real numbers t with unique \{-1, 0, 1\}-code such that the intersections Γβ ∩ (Γ β+t) are self-similar sets. For a given β ∈ (1/3, 1/2), a criterion is obtained to check whether or not a t ∈ [-1, 1] has the unique \{-1, 0, 1\}-code from both geometric and algebraic views.",

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AU - Zou, Yuru

AU - Lu, Jian

AU - Li, Wenxia

PY - 2008/12/1

Y1 - 2008/12/1

N2 - Let Γβ be the middle-(1 - 2β) Cantor set with β ∈ (1/3, 1/2). We give all real numbers t with unique {-1, 0, 1}-code such that the intersections Γβ ∩ (Γ β+t) are self-similar sets. For a given β ∈ (1/3, 1/2), a criterion is obtained to check whether or not a t ∈ [-1, 1] has the unique {-1, 0, 1}-code from both geometric and algebraic views.

AB - Let Γβ be the middle-(1 - 2β) Cantor set with β ∈ (1/3, 1/2). We give all real numbers t with unique {-1, 0, 1}-code such that the intersections Γβ ∩ (Γ β+t) are self-similar sets. For a given β ∈ (1/3, 1/2), a criterion is obtained to check whether or not a t ∈ [-1, 1] has the unique {-1, 0, 1}-code from both geometric and algebraic views.

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U2 - 10.1088/0951-7715/21/12/010

DO - 10.1088/0951-7715/21/12/010

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VL - 21

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EP - 2910

JO - Nonlinearity

JF - Nonlinearity

IS - 12

ER -

Self-similar structure on the intersection of middle-(1 - 2β) Cantor sets with β ∈ (1/3, 1/2)

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