Topological prevalence of variable speed of convergence in the deterministic chaos game
Abstract Let A be the attractor of a Banach contractive iterated function system (IFS) on a complete space. We prove that the orbit generated by a typical (in the sense of Baire category) driver recovers A with every possible speed. Our result extends the one from the paper: Leśniak et al. (Chaos 32(1):013110, 2022). We also show that our result is optimal from a certain point of view.
Authors
- Filip Strobin (ORCID: https://orcid.org/0000-0002-8671-9053)
- Krzysztof Leśniak (ORCID: https://orcid.org/0000-0001-5992-488X)
- Nina Snigireva (ORCID: https://orcid.org/0000-0002-6372-2268)
Institutions
- Ollscoil na Gaillimhe – University of Galway (IE)
- Lodz University of Technology (PL)
- Nicolaus Copernicus University (PL)
- Institute of Mathematics (PL)
Publication Details
- Journal
- Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas
- Published
- 2024-08-30
- DOI
- https://doi.org/10.1007/s13398-024-01658-0
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00