Understanding the limit sets generated by general iterated function systems on unbounded spaces

2023/03/30 by Kanji Inui, Inui, Kanji
Mathematics · #28A80 #Dynamical Systems (math.DS) #FOS: Mathematics #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.2303.17153

openalex publication_date 2023/03/30 · openalex created_date 2023/04/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we reformulate the definition of the iterated function systems (denoted by general IFSs in this paper) and show the existence and uniqueness (in some sense) of the limit sets generated by the general IFSs, to unify the definitions of the limit sets introduced before. Note that the general IFSs are defined on (possibly unbounded) complete metric spaces and we instead assume a ``natural" condition of general IFSs to show the main result. To obtain the main result, we apply techniques in the Banach fixed point theorem to the general IFSs with the ``natural" condition. Besides, we consider an example of general IFSs.

Related

• On generalized iterated function systems defined on ℓ_∞-sum of a metric space
• On the convergence of sequences in the space of n-iterated function systems with applications
• The Hutchinson-Barnsley theory for infinite iterated function systems
• On iterated function systems and algebraic properties of Lipschitz maps in partial metric spaces
• On a typical compact set as the attractor of generalized iterated\n function systems of infinite order