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^*

^*此作品的通讯作者

数学科学学院

Beihang University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
页（从-至）	938-974
页数	37
期刊	Acta Mathematica Sinica, English Series
卷	41
期	3
DOI	https://doi.org/10.1007/s10114-025-3326-z
出版状态	已出版 - 3月 2025

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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

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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.

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KW - 28A80

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Tangent Measures of Homogeneous Cantor Sets Satisfying the Strong Separation Condition

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