On the Space of Iterated Function Systems and Their Topological StabilityOn the Space of Iterated Function Systems and Their Topological StabilityA. Arbieto, A. Trilles

被引：0

作者：

Alexander Arbieto ^{[1
]}

Alexandre Trilles ^{[2
]}

机构：

[1] Universidade Federal do Rio de Janeiro,Instituto de Matemática

[2] Jagiellonian University,Doctoral School of Exact and Natural Sciences

[3] Jagiellonian University,Faculty of Mathematics and Computer Science

来源：

Qualitative Theory of Dynamical Systems | 2025年 / 24卷 / 2期

关键词：

Iterated function systems; Topological stability; Shadowing; Expansiveness; Primary 37B25; Secondary 37B05;

D O I：

10.1007/s12346-025-01250-w

中图分类号：

学科分类号：

摘要：

We study iterated function systems with compact parameter space (IFS for short). We show that the space of IFS with phase space X is the hyperspace of the space of continuous maps from X to itself, which allows us to use the Hausdorff metric to define topological stability for IFS. We then prove that the concordant shadowing property is a necessary condition for topological stability and it is a sufficient condition if the IFS is expansive. Additionally, we provide an example to show that the concordant shadowing property is genuinely different from the traditional notion that, in our setting, becomes too weak.

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