TANGENT MEASURES ON HOMOGENEOUS CANTOR SETS ON ℝ SATISFYING THE CONVEX OPEN SET CONDITION

Yongtao Wang; Yumei Xue

doi:10.1142/S0218348X25500185

TANGENT MEASURES ON HOMOGENEOUS CANTOR SETS ON ℝ SATISFYING THE CONVEX OPEN SET CONDITION

Yongtao Wang
, Yumei Xue^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

Abstract

This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝ satisfying the convex open set condition, a similar problem has been discussed in our previous work but with the strong separation condition. Through the dynamics of "zooming in"on any typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝ.

Original language	English
Article number	2550018
Journal	Fractals
Volume	33
Issue number	1
DOIs	https://doi.org/10.1142/S0218348X25500185
State	Published - 2025

Keywords

Homogeneous Cantor Sets
Limit Models
Tangent Measures
The Convex Open Set Condition

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10.1142/S0218348X25500185

Cite this

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abstract = "This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝ satisfying the convex open set condition, a similar problem has been discussed in our previous work but with the strong separation condition. Through the dynamics of {"}zooming in{"}on any typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝ.",

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N2 - This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝ satisfying the convex open set condition, a similar problem has been discussed in our previous work but with the strong separation condition. Through the dynamics of "zooming in"on any typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝ.

AB - This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝ satisfying the convex open set condition, a similar problem has been discussed in our previous work but with the strong separation condition. Through the dynamics of "zooming in"on any typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝ.

KW - Homogeneous Cantor Sets

KW - Limit Models

KW - Tangent Measures

KW - The Convex Open Set Condition

UR - https://www.scopus.com/pages/publications/85217626210

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DO - 10.1142/S0218348X25500185

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SN - 0218-348X

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TANGENT MEASURES ON HOMOGENEOUS CANTOR SETS ON ℝ SATISFYING THE CONVEX OPEN SET CONDITION

Abstract

Keywords

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