Rocky Mountain Journal of Mathematics

Hartman-Grobman theorem for iterated function systems

Mehdi Fatehi Nia and Fatemeh Rezaei

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Abstract

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

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

Dates
First available in Project Euclid: 10 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1552186963

Digital Object Identifier
doi:10.1216/RMJ-2019-49-1-307

Mathematical Reviews number (MathSciNet)
MR3921878

Zentralblatt MATH identifier
07036629

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

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

Citation

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. https://projecteuclid.org/euclid.rmjm/1552186963


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