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Research Article | Open Access

On iterated function systems with inverses

Department of Mathematics, Saitama University, Saitama, Japan
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Abstract

In this article we consider iterated function systems that contain inverse maps, which we call IFS with inverses. We show that the invariant measures for IFS with inverses agree with the invariant measures for associated graph-directed IFS under the suitable choice of weight.

Keywords

iterated function systemsabsolute continuityrandom walks on groups
CLC number: 28A80, 37D20

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 9034-9041
DOI: 10.3934/math.2025415

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Takahashi Y. On iterated function systems with inverses. AIMS Mathematics, 2025, 10(4): 9034-9041. https://doi.org/10.3934/math.2025415

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Received: 28 December 2024
Revised: 18 March 2025
Accepted: 25 March 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)