Geodesic
On the Hausdorff dimension faithfulness of Oppenheim expansion
Yu Sun1 ; Zhengliang Zhang2 ; Jia Liu3
1Faculty of Science JiangSu University 212013, Zhenjiang, P.R. China
2School of Mathematical Sciences Henan Institute of Science and Technology 453003, Xinxiang, P.R. China
3Institute 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
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 
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     title = {On the {Hausdorff} dimension faithfulness of {Oppenheim} expansion},
     journal = {Acta Arithmetica},
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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

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