Asymptotic behavior of distribution of frequencies of digits

• Autores: Luis M. Barreira, Clàudia Valls Anglès
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 1, 2008, págs. 177-196
• Idioma: inglés
• DOI: 10.1017/s0305004108001254
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• Resumen

  • 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.