Intersection of translations of cantor triadic set 1

Wenxia Li; Dongmei Xiao

doi:10.1016/s0252-9602(17)30631-8

Intersection of translations of cantor triadic set 1

Wenxia Li^*
, Dongmei Xiao

^*Corresponding author for this work

Central China Normal University

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Let C be the Cantor triadic set and let C_α = C + α = {β+α : β ∈ C} for -1 ≤ α ≤ 1. Let H_p = {α ∈ C : dim_H(C_α ∩ C) = dim_B(C_α ∩ C) = (1 - p) log 2/log 3}, 0 < p < 1. The authors give the dimensions of C_α ∩ C and H_p. In addition the characteristic of H_p is described by means of some measure μ supported on C.

Original language	English
Pages (from-to)	214-219
Number of pages	6
Journal	Acta Mathematica Scientia
Volume	19
Issue number	2
DOIs	https://doi.org/10.1016/s0252-9602(17)30631-8
State	Published - Apr 1999
Externally published	Yes

Keywords

Cantor triadic set
Generalized Moran set
Multifractal decomposition, point-wise dimension

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10.1016/s0252-9602(17)30631-8

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title = "Intersection of translations of cantor triadic set 1",

abstract = "Let C be the Cantor triadic set and let Cα = C + α = \{β+α : β ∈ C\} for -1 ≤ α ≤ 1. Let Hp = \{α ∈ C : dimH(Cα ∩ C) = dimB(Cα ∩ C) = (1 - p) log 2/log 3\}, 0 < p < 1. The authors give the dimensions of Cα ∩ C and Hp. In addition the characteristic of Hp is described by means of some measure μ supported on C.",

keywords = "Cantor triadic set, Generalized Moran set, Multifractal decomposition, point-wise dimension",

author = "Wenxia Li and Dongmei Xiao",

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AU - Li, Wenxia

AU - Xiao, Dongmei

PY - 1999/4

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N2 - Let C be the Cantor triadic set and let Cα = C + α = {β+α : β ∈ C} for -1 ≤ α ≤ 1. Let Hp = {α ∈ C : dimH(Cα ∩ C) = dimB(Cα ∩ C) = (1 - p) log 2/log 3}, 0 < p < 1. The authors give the dimensions of Cα ∩ C and Hp. In addition the characteristic of Hp is described by means of some measure μ supported on C.

AB - Let C be the Cantor triadic set and let Cα = C + α = {β+α : β ∈ C} for -1 ≤ α ≤ 1. Let Hp = {α ∈ C : dimH(Cα ∩ C) = dimB(Cα ∩ C) = (1 - p) log 2/log 3}, 0 < p < 1. The authors give the dimensions of Cα ∩ C and Hp. In addition the characteristic of Hp is described by means of some measure μ supported on C.

KW - Cantor triadic set

KW - Generalized Moran set

KW - Multifractal decomposition, point-wise dimension

UR - https://www.scopus.com/pages/publications/0007691351

U2 - 10.1016/s0252-9602(17)30631-8

DO - 10.1016/s0252-9602(17)30631-8

M3 - 文章

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EP - 219

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 2

ER -

Intersection of translations of cantor triadic set 1

Abstract

Keywords

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