ON DIGIT FREQUENCIES IN β-EXPANSIONS

被引：8

作者：

Boyland, Philip ^{[1
]}

de Carvalho, Andre ^{[2
]}

Hall, Toby ^{[3
]}

机构：

[1] Univ Florida, Dept Math, 372 Little Hall, Gainesville, FL 32611 USA

[2] IME USP, Dept Matemat Aplicada, Rua Matao 1010,Cidade Univ, BR-05508090 Sao Paulo, SP, Brazil

[3] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside, England

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 368卷 / 12期

基金：

巴西圣保罗研究基金会;

关键词：

NUMBERS; SHIFTS; SETS;

D O I：

10.1090/tran/6617

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the sets DF(beta) of digit frequencies of beta-expansions of numbers in [0, 1]. We show that DF(beta) is a compact convex set with countably many extreme points which varies continuously with beta; that there is a full measure collection of non-trivial closed intervals on each of which DF(beta) mode locks to a constant polytope with rational vertices; and that the generic digit frequency set has infinitely many extreme points, accumulating on a single non-rational extreme point whose components are rationally independent.

引用

页码：8633 / 8674

页数：42

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