ON A GENERALIZED SELF-SIMILARITY IN THE p-ADIC FIELD

被引：2

作者：

Mukhamedov, Farrukh ^{[1
]}

Khakimov, Otabek ^{[2
]}

机构：

[1] Int Islamic Univ Malaysia, Fac Sci, Dept Computat & Theoret Sci, POB 141, Kuantan 25710, Pahang, Malaysia

[2] Natl Univ Uzbekistan, Inst Math, 29 Dormon Yoli Str, Tashkent 100125, Uzbekistan

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2016年 / 24卷 / 04期

关键词：

p-Adic Numbers; Unconventional Limit Set; Compact; Uniformly Perfect; Quasi-Symmetric; Symbolic Cantor Set; STATE POTTS-MODEL; CAYLEY TREE; DYNAMICAL-SYSTEMS; GIBBS MEASURES; PHASE-TRANSITIONS; SETS; CHAOS;

D O I：

10.1142/S0218348X16500419

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, we introduce a new set which defines a generalized self similar set or contractive functions {f(i)}(N) (i=1) on the unit ball Z(p) of p-adic numhers. This set is called unconventional limit set. We prove that the unconventional limit set is compact, perfect and uniformly disconnected. Moreover, we provide an example of two contractions for which the corresponding unconventional limiting set is quasi-symmetrically equivalent to the symbolic Cantor set.

引用

页数：11

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