A closed graph theorem for hyperbolic iterated function systems

被引：0

作者：

Mundey, Alexander ^{[1
]}

机构：

[1] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW 2522, Australia

来源：

JOURNAL OF FRACTAL GEOMETRY | 2022年 / 9卷 / 3-4期

关键词：

Iterated function system; closed graph theorem; hyperbolic; fractal; morphism; conjugacy;

D O I：

10.4171/JFG/116

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, we introduce the notion of a morphism between two hyperbolic iterated function systems. We prove that the graph of such a morphism is the attractor of an iterated function system, giving a closed graph theorem, and demonstrate how it can be used to approach the topological conjugacy problem for iterated function systems.

引用

页码：325 / 336

页数：12

共 15 条

[1]

[Anonymous], 2001, Analysis on Fractals

[2]

[Anonymous], 2006, Superfractals

[3]

Barnsley M. F., 2014, RECENT PROGR GEN TOP, VIII, P69

[4] Transformations between Self-Referential Sets [J].

Barnsley, Michael F. .

AMERICAN MATHEMATICAL MONTHLY, 2009, 116 (04) :291-304

[5] SUB-SELF-SIMILAR SETS [J].

FALCONER, KJ .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 347 (08) :3121-3129

[6]

Hata M., 1985, Japan J. Appl. Math., V2, P381

[7]

Hu S, 1997, HDB MULTIVALUED ANAL

[8] FRACTALS AND SELF SIMILARITY [J].

HUTCHINSON, JE .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1981, 30 (05) :713-747

[9]

Kameyama A, 2000, J MATH KYOTO U, V40, P601

[10]

Kameyama A., 1993, JAPAN J IND APPL MAT, V10, P85, DOI DOI 10.1007/BF03167204

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