Tangent Measures of Homogeneous Cantor Sets Satisfying the Strong Separation Condition

Xiangyu Liang; Yongtao Wang

doi:10.1007/s10114-025-3326-z

Tangent Measures of Homogeneous Cantor Sets Satisfying the Strong Separation Condition

Xiangyu Liang
, Yongtao Wang^*

^*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^d generated by specific iterated function systems that satisfy the strong separation condition. Through the dynamics of “zooming in” on typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝ^d.

Original language	English
Pages (from-to)	938-974
Number of pages	37
Journal	Acta Mathematica Sinica, English Series
Volume	41
Issue number	3
DOIs	https://doi.org/10.1007/s10114-025-3326-z
State	Published - Mar 2025

Keywords

28A33
28A78
28A80
Homogeneous Cantor sets
limit models
tangent measures

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10.1007/s10114-025-3326-z

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abstract = "This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝd generated by specific iterated function systems that satisfy the strong separation condition. Through the dynamics of “zooming in” on typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝd.",

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PY - 2025/3

Y1 - 2025/3

N2 - This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝd generated by specific iterated function systems that satisfy the strong separation condition. Through the dynamics of “zooming in” on typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝd.

AB - This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝd generated by specific iterated function systems that satisfy the strong separation condition. Through the dynamics of “zooming in” on typical point, we derive an explicit and uniform formula for the tangent measures associated with this category of homogeneous Cantor sets on ℝd.

KW - 28A33

KW - 28A78

KW - 28A80

KW - Homogeneous Cantor sets

KW - limit models

KW - tangent measures

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U2 - 10.1007/s10114-025-3326-z

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JF - Acta Mathematica Sinica, English Series

IS - 3

ER -

Tangent Measures of Homogeneous Cantor Sets Satisfying the Strong Separation Condition

Abstract

Keywords

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