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

Krzysztof Leśniak; Nina Snigireva; Filip Strobin

doi:10.1007/s13398-024-01658-0

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

Krzysztof Leśniak
, Nina Snigireva
, Filip Strobin

Mathematics

Nicolaus Copernicus University
Lodz University of Technology

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

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.

Original language	English
Article number	157
Journal	Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume	118
Issue number	4
DOIs	https://doi.org/10.1007/s13398-024-01658-0
Publication status	Published - Oct 2024

Keywords

Chaos game
Driver
Iterated function system
Lower box dimension
Primary 28A80
Residual set
Secondary 37H12

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10.1007/s13398-024-01658-0

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KW - Iterated function system

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KW - Primary 28A80

KW - Residual set

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ER -

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

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