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