On the maximal run-length function in the Lüroth expansion

Yu Sun; Jian Xu

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 1, page 277-291
  • ISSN: 0011-4642

Abstract

top
We obtain a metrical property on the asymptotic behaviour of the maximal run-length function in the Lüroth expansion. We also determine the Hausdorff dimension of a class of exceptional sets of points whose maximal run-length function has sub-linear growth rate.

How to cite

top

Sun, Yu, and Xu, Jian. "On the maximal run-length function in the Lüroth expansion." Czechoslovak Mathematical Journal 68.1 (2018): 277-291. <http://eudml.org/doc/294301>.

@article{Sun2018,
abstract = {We obtain a metrical property on the asymptotic behaviour of the maximal run-length function in the Lüroth expansion. We also determine the Hausdorff dimension of a class of exceptional sets of points whose maximal run-length function has sub-linear growth rate.},
author = {Sun, Yu, Xu, Jian},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lüroth expansion; run-length function; Hausdorff dimension},
language = {eng},
number = {1},
pages = {277-291},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the maximal run-length function in the Lüroth expansion},
url = {http://eudml.org/doc/294301},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Sun, Yu
AU - Xu, Jian
TI - On the maximal run-length function in the Lüroth expansion
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 277
EP - 291
AB - We obtain a metrical property on the asymptotic behaviour of the maximal run-length function in the Lüroth expansion. We also determine the Hausdorff dimension of a class of exceptional sets of points whose maximal run-length function has sub-linear growth rate.
LA - eng
KW - Lüroth expansion; run-length function; Hausdorff dimension
UR - http://eudml.org/doc/294301
ER -

References

top
  1. Dajani, K., Kraaikamp, C., Ergodic Theory of Numbers, Carus Mathematical Monographs 29, Mathematical Association of America, Washington (2002). (2002) Zbl1033.11040MR1917322
  2. Erdős, P., Rényi, A., 10.1007/BF02795493, J. Anal. Math. 23 (1970), 103-111. (1970) Zbl0225.60015MR0272026DOI10.1007/BF02795493
  3. Falconer, K., Fractal Geometry: Mathematical Foundations and Applications, Wiley & Sons, Chichester (1990). (1990) Zbl0689.28003MR1102677
  4. Galambos, J., 10.1007/BFb0081642, Lecture Notes in Mathematics 502, Springer, Berlin (1976). (1976) Zbl0322.10002MR0568141DOI10.1007/BFb0081642
  5. Hutchinson, J. E., 10.1512/iumj.1981.30.30055, Indiana Univ. Math. J. 30 (1981), 713-747. (1981) Zbl0598.28011MR0625600DOI10.1512/iumj.1981.30.30055
  6. Kesseböhmer, M., Munday, S., Stratmann, B. O., 10.1515/9783110439427, De Gruyter Graduate, De Gruyter, Berlin (2016). (2016) Zbl1362.37003MR3585883DOI10.1515/9783110439427
  7. Li, J., Wu, M., 10.1016/j.jmaa.2015.12.001, J. Math. Anal. Appl. 436 (2016), 355-365. (2016) Zbl06536909MR3440098DOI10.1016/j.jmaa.2015.12.001
  8. Li, J., Wu, M., 10.1007/s00605-016-0977-y, Monatsh. Math. 182 (2017), 865-875. (2017) Zbl06704122MR3624949DOI10.1007/s00605-016-0977-y
  9. Lüroth, J., 10.1007/BF01443883, Math. Ann. 21 (1883), 411-423 German 9999JFM99999 15.0187.01. (1883) MR1510205DOI10.1007/BF01443883
  10. Ma, J.-H., Wen, S.-Y., Wen, Z.-Y., 10.1007/s00605-007-0455-7, Monatsh. Math. 151 (2007), 287-292. (2007) Zbl1170.28001MR2329089DOI10.1007/s00605-007-0455-7
  11. Moran, P. A. P., 10.1017/s0305004100022684, Proc. Camb. Philos. Soc. 42 (1946), 15-23. (1946) Zbl0063.04088MR0014397DOI10.1017/s0305004100022684
  12. Révész, P., 10.1142/5847, World Scientific, Hackensack (2005). (2005) Zbl1090.60001MR2168855DOI10.1142/5847
  13. Sun, Y., Xu, J., 10.1007/s00605-016-0974-1, Monatsh. Math. 184 (2017), 291-296. (2017) Zbl06788682MR3696113DOI10.1007/s00605-016-0974-1
  14. Wang, B. W., Wu, J., On the maximal run-length function in continued fractions, Annales Univ. Sci. Budapest., Sect. Comp. 34 (2011), 247-268. (2011) 
  15. Zou, R., 10.1007/s10587-011-0055-5, Czech. Math. J. 61 (2011), 881-888. (2011) Zbl1249.11085MR2886243DOI10.1007/s10587-011-0055-5

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.