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

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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.

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     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},
     mrnumber = {1265907},
     zbl = {0817.11037},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JTNB_1993__5_2_303_0/}
}
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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://geodesic.mathdoc.fr/item/JTNB_1993__5_2_303_0/