Geodesic
On the Hausdorff dimension faithfulness of Oppenheim expansion
Yu Sun1 ; Zhengliang Zhang2 ; Jia Liu3
1 Faculty of Science JiangSu University 212013, Zhenjiang, P.R. China
2 School of Mathematical Sciences Henan Institute of Science and Technology 453003, Xinxiang, P.R. China
3 Institute of Statistics and Applied Mathematics Anhui University of Finance and Economics 233030, Bengbu, P.R. China
Acta Arithmetica, Tome 180 (2017) no. 1, pp. 89-99

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We show that the family of cylinders generated by Oppenheim expansion is not faithful for Hausdorff dimension calculation on the unit interval. On the other hand, we prove that the family of all finite unions of consecutive cylinders of the same rank is faithful. Some special cases such as Lüroth expansion, Engel expansion and Sylvester expansion are included.
DOI : 10.4064/aa8648-2-2017
Keywords: family cylinders generated oppenheim expansion faithful hausdorff dimension calculation unit interval other prove family finite unions consecutive cylinders rank faithful special cases roth expansion engel expansion sylvester expansion included

Yu Sun 1 ; Zhengliang Zhang 2 ; Jia Liu 3

1 Faculty of Science JiangSu University 212013, Zhenjiang, P.R. China
2 School of Mathematical Sciences Henan Institute of Science and Technology 453003, Xinxiang, P.R. China
3 Institute of Statistics and Applied Mathematics Anhui University of Finance and Economics 233030, Bengbu, P.R. China 
@article{10_4064_aa8648_2_2017,
     author = {Yu Sun and Zhengliang Zhang and Jia Liu},
     title = {On the {Hausdorff} dimension faithfulness of {Oppenheim} expansion},
     journal = {Acta Arithmetica},
     pages = {89--99},
     publisher = {mathdoc},
     volume = {180},
     number = {1},
     year = {2017},
     doi = {10.4064/aa8648-2-2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8648-2-2017/}
}
TY  - JOUR
AU  - Yu Sun
AU  - Zhengliang Zhang
AU  - Jia Liu
TI  - On the Hausdorff dimension faithfulness of Oppenheim expansion
JO  - Acta Arithmetica
PY  - 2017
SP  - 89
EP  - 99
VL  - 180
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa8648-2-2017/
DO  - 10.4064/aa8648-2-2017
LA  - en
ID  - 10_4064_aa8648_2_2017
ER  - 
%0 Journal Article
%A Yu Sun
%A Zhengliang Zhang
%A Jia Liu
%T On the Hausdorff dimension faithfulness of Oppenheim expansion
%J Acta Arithmetica
%D 2017
%P 89-99
%V 180
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa8648-2-2017/
%R 10.4064/aa8648-2-2017
%G en
%F 10_4064_aa8648_2_2017
Yu Sun; Zhengliang Zhang; Jia Liu. On the Hausdorff dimension faithfulness of Oppenheim expansion. Acta Arithmetica, Tome 180 (2017) no. 1, pp. 89-99. doi: 10.4064/aa8648-2-2017

Cité par Sources :