Rocky Mountain Journal of Mathematics

Hartman-Grobman theorem for iterated function systems

Mehdi Fatehi Nia and Fatemeh Rezaei

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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 $\mathbb {R}$

Article information

Rocky Mountain J. Math., Volume 49, Number 1 (2019), 307-333.

First available in Project Euclid: 10 March 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34A34: Nonlinear equations and systems, general 34D30: Structural stability and analogous concepts [See also 37C20]

IFS topologically conjugate Lipschitz function Hartman-Grobman theorem diffeomorphism homeomorphism structural sta­bil­ity


Nia, Mehdi Fatehi; Rezaei, Fatemeh. Hartman-Grobman theorem for iterated function systems. Rocky Mountain J. Math. 49 (2019), no. 1, 307--333. doi:10.1216/RMJ-2019-49-1-307.

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