Moran-Type Iterated Function Systems and Dimensions of Moran Self-Similar Sets
Dynamical Systems
2026-01-19 v1
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.
Keywords
Cite
@article{arxiv.2601.11023,
title = {Moran-Type Iterated Function Systems and Dimensions of Moran Self-Similar Sets},
author = {Yong-Shen Cao and Qi-Rong Deng and Ming-Tian Li},
journal= {arXiv preprint arXiv:2601.11023},
year = {2026}
}