Topological prevalence of variable speed of convergence in the deterministic chaos game

• Krzysztof Leśniak ^[1] ; Nina Snigireva ^[3] ; Filip Strobin ^[2]
  1. [1] Nicolaus Copernicus University

     Nicolaus Copernicus University

     Toruń, Polonia

     
  2. [2] Lodz University of Technology

     Lodz University of Technology

     Łódź, Polonia

     
  3. [3] University of Galway, Ireland

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• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 118, Nº. 4, 2024
• Idioma: inglés
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• Resumen

  • 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: Le´sniak et al. (Chaos 32(1):013110, 2022). We also show that our result is optimal from a certain point of view