The R-IFSs and their attractors

2023/05/05 by Hung Nguyen Viet, Viet, Hung Nguyen, Duy Bui The +3
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2305.03426

openalex publication_date 2023/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper introduces a new class of iterated function systems (IFSs) called R-IFSs, which include both rotation/reflection maps and contraction maps. The study of R-IFSs is motivated by the recent research direction on enriching IFSs by adding other types of mappings. The paper investigates the existence and properties of the semi-attractor and compact invariant sets of R-IFSs, as well as the class of minimal invariant sets of R-IFSs. The paper also provides a familiar setting that is an invariant set of R-IFS but not an invariant set of any IFS.

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