On digit frequencies in beta-expansions


Boyland, P, de Carvalho, A and Hall, T (2016) On digit frequencies in beta-expansions. Transactions of the American Mathematical Society (TRAN), 368 (12). pp. 8633-8674.

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Abstract

We study the sets DF(β) of digit frequencies of β-expansions of numbers in [0,1]. We show that DF(β) is a compact convex set with countably many extreme points which varies continuously with β; that there is a full measure collection of non-trivial closed intervals on each of which DF(β) 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.

Item Type: Article
Additional Information: ## TULIP Type: Articles/Papers (Journal) ##
Depositing User: Symplectic Admin
Date Deposited: 08 Feb 2016 08:57
Last Modified: 17 Dec 2022 01:38
DOI: 10.1090/tran/6617
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/2050279

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