The Invariant Measure for a Countable Generalized Iterated Function System

被引：0
作者：
Abraham, Izabella [1 ]
机构：
[1] Transilvania Univ, Fac Math & Comp Sci, Iuliu Maniu 50, Brasov 500091, Romania
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2024年 / 21卷 / 07期
关键词：
Generalized iterated function system; countable generalized iterated function system; invariant measure; Monge-Kantorovich distance; ATTRACTORS; IFS;
D O I：
10.1007/s00009-024-02751-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this paper is to answer one of the open questions raised in Strobin [Qual. Theory Dyn. Syst. 19, 85 (2020)] of whether there exists an invariant (Hutchinson) measure for generalized iterated function systems of any order, consisting of a countably infinite number of maps. Our results likewise strengthen those obtained in Secelean [Mediterr. J. Math. 11, 361-372 (2014)], where the existence of the invariant measure is ascertained only for the case of generalized iterated function systems of order 2, consisting of functions which satisfy a particular contractive condition.
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页数：22
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