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arXiv · 1308.4437

On digit frequencies in β-expansions

Philip Boyland·André de Carvalho·Toby Hall
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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.

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Philip Boyland, André de Carvalho, Toby Hall. 2014-09-01. On digit frequencies in β-expansions. https://arxiv.org/abs/1308.4437

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