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<p>This paper investigates tangent measures in the sense of Preiss for homogeneous Cantor sets on ℝ<sup><i>d</i></sup> 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<sup><i>d</i></sup>.</p>

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Tangent Measures of Homogeneous Cantor Sets Satisfying the Strong Separation Condition

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Xiangyu Liang,
  • Yongtao Wang

摘要

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.