Generalized Hausdorff dimensions of sets of real numbers with zero entropy expansion

Abstract : The complexity function of an infinite word w on a finite alphabet A is the sequence counting, for each non-negative integer n, the number of words of length n on the alphabet A that are factors of the infinite word w. Let f be a given function with subexponential growth. The goal of this work is to estimate the generalized Hausdorff dimensions of the set of real numbers whose q-adic expansion has a complexity function bounded by f and the set of real numbers whose continued fraction expansion is bounded by q and has a complexity function bounded by f.
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Submitted on : Wednesday, February 10, 2016 - 3:21:49 PM
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Christian Mauduit, Carlos Gustavo Moreira. Generalized Hausdorff dimensions of sets of real numbers with zero entropy expansion. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2012, 32 (03), pp.1073-1089. ⟨10.1017/S0143385711000137⟩. ⟨hal-01272296⟩

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