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
相关论文
共 33 条
[1]   Generalized Iterated Function Systems on b-Metric Spaces [J].
Abraham, Izabella ;
Miculescu, Radu .
MATHEMATICS, 2023, 11 (13)
[2]  
BARNSLEY MF, 1988, FRACTALS EVERYWHERE
[3]  
Bogachev VI., 2007, Measure theory, VI, II, P500, DOI DOI 10.1007/978-3-540-34514-5
[4]  
Chitescu I., 1983, Spatii de functii
[5]   Topological version of generalized (infinite) iterated function systems [J].
Dumitru, Dan ;
Ioana, Loredana ;
Sfetcu, Razvan-Cornel ;
Strobin, Filip .
CHAOS SOLITONS & FRACTALS, 2015, 71 :78-90
[6]  
FERNAU H, 1994, MATH NACHR, V170, P79
[7]  
García G, 2020, MEDITERR J MATH, V17, DOI 10.1007/s00009-020-01585-5
[8]  
Guzik G., 2023, Banach Cent. Publ, V125, P23, DOI [10.4064/bc125-3, DOI 10.4064/BC125-3]
[9]   On the geometric ergodicity for a generalized IFS with probabilities [J].
Guzik, Grzegorz ;
Kapica, Rafal .
STOCHASTICS AND DYNAMICS, 2022, 22 (01)
[10]   The Hutchinson-Barnsley theory for infinite iterated function systems [J].
Gwozdz-Lukawska, G ;
Jachymski, J .
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2005, 72 (03) :441-454
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