THE HAUSDORFF DIMENSION FUNCTION OF THE FAMILY OF CONFORMAL ITERATED FUNCTION SYSTEMS OF GENERALIZED COMPLEX CONTINUED FRACTIONS

被引：2

作者：

Inui, Kanji ^{[1
]}

Okada, Hikaru ^{[2
]}

Sumi, Hiroki ^{[1
]}

机构：

[1] Kyoto Univ, Course Math Sci, Dept Human Coexistence, Grad Sch Human & Environm Studies,Sakyo Ku, Yoshida Nihonmatsu Cho, Kyoto 6068501, Japan

[2] Osaka Univ, Grad Sch Sci, Dept Math, 1-1 Machikaneyama Cho, Toyonaka, Osaka 5600043, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 02期

关键词：

Infinite conformal iterated function systems; fractal geometry; limit sets; Hausdorff dimension; generalized complex continued fractions; SELF; FRACTALS;

D O I：

10.3934/dcds.2020060

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the family of CIFSs of generalized complex continued fractions with a complex parameter space. This is a new interesting example to which we can apply a general theory of infinite CIFSs and analytic families of infinite CIFSs. We show that the Hausdorff dimension function of the family of the CIFSs of generalized complex continued fractions is continuous in the parameter space and is real-analytic and subharmonic in the interior of the parameter space. As a corollary of these results, we also show that the Hausdorff dimension function has a maximum point and the maximum point belongs to the boundary of the parameter space.

引用

页码：753 / 766

页数：14

共 50 条

[21] Hausdorff dimension of an exceptional set in the theory of continued fractions*
Bakhtawar, Ayreena
Bos, Philip
Hussain, Mumtaz
NONLINEARITY, 2020, 33 (06) : 2615 - 2639
[22] Cyclic generalized iterated function systems
Pasupathi, Rajan
Chand, Arya Kumar Bedabrata
Navascues, Maria Antonia
Sebastian, Maria Victoria
COMPUTATIONAL AND MATHEMATICAL METHODS, 2021, 3 (06)
[23] Separation conditions for conformal iterated function systems
Lau, Ka-Sing
Ngai, Sze-Man
Wang, Xiang-Yang
MONATSHEFTE FUR MATHEMATIK, 2009, 156 (04): : 325 - 355
[24] A class of iterated function systems with adapted piecewise constant transition probabilities: Asymptotic stability and Hausdorff dimension of the invariant measure
Dubarry, Blandine
CHAOS SOLITONS & FRACTALS, 2017, 103 : 602 - 612
[25] On the Exponential Growth of Norms in Semigroups of Linear Endomorphisms and the Hausdorff Dimension of Attractors of Projective Iterated Function Systems
De Leo, Roberto
JOURNAL OF GEOMETRIC ANALYSIS, 2015, 25 (03) : 1798 - 1827
[26] On the Exponential Growth of Norms in Semigroups of Linear Endomorphisms and the Hausdorff Dimension of Attractors of Projective Iterated Function Systems
Roberto De Leo
The Journal of Geometric Analysis, 2015, 25 : 1798 - 1827
[27] Tiling iterated function systems
Barnsley, Louisa F.
Barnsley, Michael F.
Vince, Andrew
CHAOS SOLITONS & FRACTALS, 2024, 182
[28] PERTURBED ITERATED FUNCTION SYSTEMS AND THE EXACT HAUSDORFF MEASURE OF THEIR ATTRACTORS
Freeman, Nicholas
REAL ANALYSIS EXCHANGE, 2009, 35 (01) : 91 - 119
[29] Quantitative recurrence properties in conformal iterated function systems
Seuret, S.
Wang, B. -W.
ADVANCES IN MATHEMATICS, 2015, 280 : 472 - 505
[30] HAUSDORFF DIMENSION OF SETS OF DIVERGENCE ARISING FROM CONTINUED FRACTIONS
Short, Ian
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (04) : 1371 - 1385

← 1 2 3 4 5 →