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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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