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arXiv · 2601.11023

Moran-Type Iterated Function Systems and Dimensions of Moran Self-Similar Sets

Yong-Shen Cao·Qi-Rong Deng·Ming-Tian Li
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Abstract

Moran-type iterated function systems (Moran-type IFS or MIFS) are defined by a sequence of iterated function systems, and their basic theoretical framework is established. We define Moran-type attractors and invariant probability measures associated with a sequence of probability weight vectors. Furthermore, separation conditions for MIFS are introduced, and the dimension theory of Moran-type self-similar sets is investigated. Appropriate examples are provided to illustrate and support the definitions and results.

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Yong-Shen Cao, Qi-Rong Deng, Ming-Tian Li. 2026-01-16. Moran-Type Iterated Function Systems and Dimensions of Moran Self-Similar Sets. https://arxiv.org/abs/2601.11023

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