Addendum and corrigendum to "On the chaos game of iterated function systems"

Pablo G. Barrientos, Maxwell Fitzsimmons, Fatemeh H. Ghane, Dominique Malicet, Aliasghar Sarizadeh



We provide a counter-example to Theorem 1.4(a) in Topol. Methods Nonlinear Anal. 49 (2017), no. 1, 105-132, by showing that the closure of the $\Gamma$-orbit of a point $x$ in the pointwise basin of $\mathrm{Ls}$-attraction of a quasi-attractor $A$ is not compact. In order to fix this gap, we modified the definition of $\mathrm{Ls}$-basin of attraction. In addiction, we propose a better place to play the chaos game and as a consequence we get some additional results on strongly-fibred quasi-attractors and Conley attractors.


Iterated function systems; quasi-attractors; Conley attractors; chaos game

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M.F. Barnsley and K. Leśniak, The chaos game on a general iterated function system from a topological point of view, Internat. J. Bifur. Chaos 24 (2014).

M.F. Barnsley and A. Vince The Conley attractors of an iterated function system, Bull. Aust. Math. Soc. 88 (2013), 267–279.

P.G. Barrientos, F.H. Ghane, D. Malicet and A. Sarizadeh, On the chaos game of iterated function systems, Topol. Methods Nonlinear Anal. Volume 49 (2017), no. 1, 105–132.

L.J. Díaz and E. Matias, Non-hyperbolic iterated function systems: semifractals and the chaos game, Fundamenta Mathematicae 250 (2020), 21-39.

G.A. Edgar, Measure, Topology and Fractal Geometry, Undergrad. Texts Math. (1990)

J. Jachymski, L. Gajek and P. Pokarowski, The Tarski–Kantorovitch prinicple and the theory of iterated function systems, Bull. Aust. Math. Soc. 61 (2000), no. 2, 247–261.

V. Kleptsyn, Y. Kudryashov and A. Okunev, Classification of generic semigroup actions of circle diffeomorphisms, arXiv:1804.00951, (2018), preprint.

A. Lasota and J. Myjak, Semifractals, Bull. Polish Acad. Sci. Math. 44 (1996), 5–21.


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