Sums of convex compacta as attractors of hyperbolic IFS&rsquo;s

Gutsu Valeriu

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GUTSU, Valeriu. Sums of convex compacta as attractors of hyperbolic IFS’s. In: Topological Methods in Nonlinear Analysis, 2019, nr. 2(54), pp. 967-978. ISSN 1230-3429. DOI: https://doi.org/10.12775/TMNA.2019.097

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Topological Methods in Nonlinear Analysis

Numărul 2(54) / 2019 / ISSN 1230-3429

Sums of convex compacta as attractors of hyperbolic IFS’s

DOI:https://doi.org/10.12775/TMNA.2019.097

Pag. 967-978

Gutsu Valeriu

Moldova State University

Disponibil în IBN: 7 aprilie 2020

Rezumat

We prove that a finite union of convex compacta in ℝⁿ may be represented as the attractor of a hyperbolic IFS. If such a union is the condensation set for some hyperbolic IFS with condensation, then its attractor can be represented as the attractor of a standard hyperbolic IFS. We illustrate this result with the hyperbolic IFS with condensation, whose attractor is the well-known “The Pythagoras tree” fractal.

Cuvinte-cheie
Attractor, Convex set, Iterated function system, Pythagoras tree

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<dc:creator>Guţu, V.</dc:creator>
<dc:date>2019-12-25</dc:date>
<dc:description xml:lang='en'><p>We prove that a finite union of convex compacta in ℝ<sup>n</sup>&nbsp;may be represented as the attractor of a hyperbolic IFS. If such a union is the condensation set for some hyperbolic IFS with condensation, then its attractor can be represented as the attractor of a standard hyperbolic IFS. We illustrate this result with the hyperbolic IFS with condensation, whose attractor is the well-known &ldquo;The Pythagoras tree&rdquo; fractal.</p></dc:description>
<dc:identifier>10.12775/TMNA.2019.097</dc:identifier>
<dc:source>Topological Methods in Nonlinear Analysis 54 (2) 967-978</dc:source>
<dc:subject>Attractor</dc:subject>
<dc:subject>Convex set</dc:subject>
<dc:subject>Iterated function system</dc:subject>
<dc:subject>Pythagoras tree</dc:subject>
<dc:title>Sums of convex compacta as attractors of hyperbolic IFS&rsquo;s</dc:title>
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