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

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

DOI: http://dx.doi.org/10.12775/TMNA.2019.107

Abstract


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.

Keywords


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

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References


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