Non literal tranducers and some problems of normality
Journal de Théorie des Nombres de Bordeaux, Tome 5 (1993) no. 2, pp. 303-321.

A new proof of Maxfield’s theorem is given, using automata and results from Symbolic Dynamics. These techniques permit to prove that points that are near normality to base ${p}^{k}$ (resp. $p$) are also near normality to base $p$ (resp. ${p}^{k}$), and to study genericity preservation for non Lebesgue measures when going from one base to the other. Finally, similar results are proved to bases the golden mean and its square.

@article{JTNB_1993__5_2_303_0,
author = {Blanchard, Fran\c{c}ois},
title = {Non literal tranducers and some problems of normality},
journal = {Journal de Th\'eorie des Nombres de Bordeaux},
pages = {303--321},
publisher = {Universit\'e Bordeaux I},
volume = {5},
number = {2},
year = {1993},
zbl = {0817.11037},
mrnumber = {1265907},
language = {en},
url = {http://www.numdam.org/item/JTNB_1993__5_2_303_0/}
}
Blanchard, François. Non literal tranducers and some problems of normality. Journal de Théorie des Nombres de Bordeaux, Tome 5 (1993) no. 2, pp. 303-321. http://www.numdam.org/item/JTNB_1993__5_2_303_0/

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