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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

ON DIGIT FREQUENCIES IN beta-EXPANSIONS

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Author(s):
Boyland, Philip ; de Carvalho, Andre ; Hall, Toby
Total Authors: 3
Document type: Journal article
Source: Transactions of the American Mathematical Society; v. 368, n. 12, p. 8633-8674, DEC 2016.
Web of Science Citations: 2
Abstract

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. (AU)

FAPESP's process: 10/09667-0 - Topological methods in low-dimensional dynamics
Grantee:André Salles de Carvalho
Support type: Research Grants - Visiting Researcher Grant - International
FAPESP's process: 11/17581-0 - Topological methods in surface dynamics: from the Hénon family to torus rotation sets
Grantee:André Salles de Carvalho
Support type: Research Grants - Visiting Researcher Grant - International