On nonlinear iterated function systems with overlaps

被引：0

作者：

Solomyak, Boris ^{[1
]}

机构：

[1] Bar Ilan Univ, Dept Math, IL-5290002 Ramat Gan, Israel

来源：

JOURNAL OF FRACTAL GEOMETRY | 2024年 / 11卷 / 3-4期

基金：

以色列科学基金会;

关键词：

non-linear iterated function system; overlap; dimension drop; PARABOLIC IFS; SELF; CONJECTURE; DIMENSIONS; SETS;

D O I：

10.4171/JFG/150

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimension of the attractor equals the conformal dimension, so that there is no "dimension drop".

引用

页码：373 / 387

页数：15

共 21 条

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[2]

Bowen Rufus., 1979, PUBL MATH LINST HAUT, V50, P11, DOI [10.1007/BF02684767, DOI 10.1007/BF02684767]

[3] On the undecidability of freeness of matrix semigroups [J].