[Note sur la singularité d'une famille de fonctions « Minkowski's question-mark » récemment introduite]
Nous mettons en évidence une erreur dans la démonstration du théroème principal dans un article récent traitant d'une famille de fonctions « Minkowski's question-mark » généralisées, stipulant que chaque membre de la famille est un homéomorphisme singulier, et nous produisons deux preuves alternatives, l'une basée sur l'ergodicité de l'application de Gauss G et de l'application α-Lüroth
We point out a mistake in the proof of the main theorem in a recent article on a family of generalized Minkowski's question-mark functions, saying that each member of the family is a singular homeomorphism, and provide two alternative proofs, one based on the ergodicity of the Gauss map G and the α-Lüroth map
Accepté le :
Publié le :
Juan Fernández Sánchez 1 ; Wolfgang Trutschnig 2
@article{CRMATH_2017__355_9_956_0, author = {Juan Fern\'andez S\'anchez and Wolfgang Trutschnig}, title = {A note on singularity of a recently introduced family of {Minkowski's} question-mark functions}, journal = {Comptes Rendus. Math\'ematique}, pages = {956--959}, publisher = {Elsevier}, volume = {355}, number = {9}, year = {2017}, doi = {10.1016/j.crma.2017.09.009}, language = {en}, }
TY - JOUR AU - Juan Fernández Sánchez AU - Wolfgang Trutschnig TI - A note on singularity of a recently introduced family of Minkowski's question-mark functions JO - Comptes Rendus. Mathématique PY - 2017 SP - 956 EP - 959 VL - 355 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2017.09.009 LA - en ID - CRMATH_2017__355_9_956_0 ER -
%0 Journal Article %A Juan Fernández Sánchez %A Wolfgang Trutschnig %T A note on singularity of a recently introduced family of Minkowski's question-mark functions %J Comptes Rendus. Mathématique %D 2017 %P 956-959 %V 355 %N 9 %I Elsevier %R 10.1016/j.crma.2017.09.009 %G en %F CRMATH_2017__355_9_956_0
Juan Fernández Sánchez; Wolfgang Trutschnig. A note on singularity of a recently introduced family of Minkowski's question-mark functions. Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 956-959. doi : 10.1016/j.crma.2017.09.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.09.009/
[1] Generalised Lüroth expansions and a family of Minkowski's question-mark functions, C. R. Acad. Sci. Paris, Ser. I, Volume 353 (2015), pp. 943-946
[2] Ergodic Theory of Numbers, Carus Mathematical Monographs, vol. 29, The Mathematical Association of America, 2002
[3] Metrical Theory of Continued Fractions, Springer Science+Business Media, Dordrecht, The Netherlands, 2002
[4] An Introduction to Ergodic Theory, Springer, New York, 1982
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