On the attractors of weakly hyperbolic IFS's with condensation

Vasile Glavan^ab, Valeriu Guţu<sup>c

a</sup> Moldova State University, Vladimir Andrunachievici Institute of Mathematics and Computer Science, Str. A. Mateevici, 60, 2009 Chişinău, Republic of Moldova
^b University of Siedlce, Institute of Mathematics, Str. Konarskiego, 2, 08-110 Siedlce, Poland
^c Moldova State University, Department of Mathematics, Str. A. Mateevici, 60, 2009 Chişinău, Republic of Moldova

Abstract: We show that for any weakly hyperbolic IFS with condensation in $\mathbb{R}^n$ whose condensation set is a union of a finite collection of convex compact sets, there exists a standard weakly hyperbolic IFS with the same attractor.

Keywords and phrases: iterated Function Systems, weak contractions, attractors, convex sets.

MSC: 28A80, 35B41, 52A20

Received: 20.09.2024

Language: English

DOI: 10.56415/basm.y2024.i1-2.p100