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PreprintarXiv licencearXiv

On the Existence of Geometrically Attracting Measures for Iterated Function Systems with Varying Sets of Transformations

  • Dawid Czapla
  • Rafał Kapica
  • Maciej Ślęczka
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Abstract

In this paper, we focus on the asymptotic behavior of random iterated functions systems, in which both the family of transformations and the distribution of selecting them vary at each step. We consider two types of dynamics: the time-inhomogeneous Markov chain arising from forward iterates and the non-Markovian process generated by backward iterates. For both settings, we provide certain criteria for the existence of a probability measure that is geometrically attracting in the bounded Lipschitz distance, independently of the initial distribution. Finally, we illustrate our results through applications to specific models involving affine transformations.

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Cite

BibTeXRIS
BibTeX
@misc{czapla2026existence,
  title = {{On the Existence of Geometrically Attracting Measures for Iterated Function Systems with Varying Sets of Transformations}},
  author = {Dawid Czapla and Rafał Kapica and Maciej Ślęczka},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29022},
  eprint = {2608.29022},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29022},
}
RIS
TY  - UNPB
TI  - On the Existence of Geometrically Attracting Measures for Iterated Function Systems with Varying Sets of Transformations
AU  - Dawid Czapla
AU  - Rafał Kapica
AU  - Maciej Ślęczka
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29022
UR  - https://arxiv.org/abs/2608.29022
AB  - In this paper, we focus on the asymptotic behavior of random iterated functions systems, in which both the family of transformations and the distribution of selecting them vary at each step. We consider two types of dynamics: the time-inhomogeneous Markov chain arising from forward iterates and the non-Markovian process generated by backward iterates. For both settings, we provide certain criteria for the existence of a probability measure that is geometrically attracting in the bounded Lipschitz distance, independently of the initial distribution. Finally, we illustrate our results through applications to specific models involving affine transformations.
ER  -