On the Hausdorff dimension of fractals given by certain expansions of real numbers (Q652232)

The author introduces an expansion by expanding the Markov-Rényi maps [\textit{H. G. Eggleston}, Q. J. Math., Oxf. Ser. 20, 31--36 (1949; Zbl 0031.20801)]. Specifically, it is considered the expansion of the reals from \((0,1]\) into a series of exponentials with base 2 and exponent the \(-(n_1+ n_2+\cdots+ n_k)\), where \(n_1,n_2,\dots, n_k,\dots\) are the digits of the continued fraction expansion. The author studies the Hausdorff dimension of the fractals related to this expansion.