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Asymptotic behavior of distribution of frequencies of digits

Published online by Cambridge University Press:  01 July 2008

LUIS BARREIRA  and
CLAUDIA VALLS
LUIS BARREIRA
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal. e-mail: [email protected] and [email protected]
CLAUDIA VALLS
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal. e-mail: [email protected] and [email protected]
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Abstract

We present an approach to compute the Hausdorff dimension of a class of sets of real numbers that are defined in terms of nonlinear relations between frequencies of digits in some integer base m. We consider the model case of quadratic perturbations, for which the computations are already rather involved. We show that the Hausdorff dimension is analytic in the parameter determining the perturbation. Our approach also allows to estimate the asymptotic behavior of the Taylor coefficients of the dimension in terms of m.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 177 - 195
Copyright
Copyright © Cambridge Philosophical Society 2008

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