| Title:
|
Some dimensional results for a class of special homogeneous Moran sets (English) |
| Author:
|
Hu, Xiaomei |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
127-135 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We construct a class of special homogeneous Moran sets, called $\{m_{k}\}$-quasi homogeneous Cantor sets, and discuss their Hausdorff dimensions. By adjusting the value of $\{m_{k}\}_{k\ge 1}$, we constructively prove the intermediate value theorem for the homogeneous Moran set. Moreover, we obtain a sufficient condition for the Hausdorff dimension of homogeneous Moran sets to assume the minimum value, which expands earlier works. (English) |
| Keyword:
|
homogeneous Moran set |
| Keyword:
|
$\{m_{k}\}$-Moran set |
| Keyword:
|
$\{m_{k}\}$-quasi homogeneous Cantor set |
| Keyword:
|
Hausdorff dimension |
| MSC:
|
28A80 |
| idZBL:
|
Zbl 06587879 |
| idMR:
|
MR3483228 |
| DOI:
|
10.1007/s10587-016-0245-2 |
| . |
| Date available:
|
2016-04-07T15:00:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144872 |
| . |
| Reference:
|
[1] Falconer, K.: Fractal Geometry. Mathematical Foundations and Applications.John Wiley & Sons, Chichester (1990). MR 1102677 |
| Reference:
|
[2] Feng, D.-J.: The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers.Adv. Math. 195 (2005), 24-101. Zbl 1078.11062, MR 2145793, 10.1016/j.aim.2004.06.011 |
| Reference:
|
[3] Feng, D., Wen, Z., Wu, J.: Some dimensional results for homogeneous Moran sets.Sci. China, Ser. A 40 (1997), 475-482. MR 1461002, 10.1007/BF02896955 |
| Reference:
|
[4] Li, J., Wu, M.: Pointwise dimensions of general Moran measures with open set condition.Sci. China, Math. 54 (2011), 699-710. Zbl 1219.28010, MR 2786709, 10.1007/s11425-011-4187-8 |
| Reference:
|
[5] Peng, F., Wen, S.: Fatness and thinness of uniform Cantor sets for doubling measures.Sci. China, Math. 54 (2011), 75-81. Zbl 1219.28001, MR 2764786, 10.1007/s11425-010-4148-7 |
| Reference:
|
[6] Rao, H., Ruan, H.-J., Wang, Y.: Lipschitz equivalence of Cantor sets and algebraic properties of contraction ratios.Trans. Am. Math. Soc. 364 (2012), 1109-1126. Zbl 1244.28015, MR 2869169, 10.1090/S0002-9947-2011-05327-4 |
| Reference:
|
[7] Wang, B.-W., Wu, J.: Hausdorff dimension of certain sets arising in continued fraction expansions.Adv. Math. 218 (2008), 1319-1339. Zbl 1233.11084, MR 2419924, 10.1016/j.aim.2008.03.006 |
| Reference:
|
[8] Wang, X. H., Wen, S. Y.: Doubling measures on Cantor sets and their extensions.Acta Math. Hung. 134 (2012), 431-438. Zbl 1265.28001, MR 2886217, 10.1007/s10474-011-0186-z |
| Reference:
|
[9] Wu, J.: On the sum of degrees of digits occurring in continued fraction expansions of Laurent series.Math. Proc. Camb. Philos. Soc. 138 (2005), 9-20. Zbl 1062.11054, MR 2127223, 10.1017/S0305004104008163 |
| Reference:
|
[10] Wu, M.: The singularity spectrum {$f(\alpha)$} of some Moran fractals.Monatsh. Math. 144 (2005), 141-155. Zbl 1061.28005, MR 2123961, 10.1007/s00605-004-0254-3 |
| . |
