## Hartman-Grobman theorem for iterated function systems.(English)Zbl 1408.37040

Summary: In this paper, for iterated function systems, we define the classic concept of the dynamical systems: topological conjugacy of diffeomorphisms. We generalize the Hartman-Grobman theorem for one-dimensional iterated function systems on $$\mathbb{R}$$ Also, we introduce the basic concept of structural stability for an iterated function system, and therefore, we investigate the necessary condition for structural stability of an iterated function system on $$\mathbb{R}$$.

### MSC:

 37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems 37C05 Dynamical systems involving smooth mappings and diffeomorphisms
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