| dc.contributor.author |
Vu, Thi Hong Thanh |
|
| dc.contributor.author |
et al. |
|
| dc.date.accessioned |
2011-06-08T13:06:18Z |
|
| dc.date.available |
2011-06-08T13:06:18Z |
|
| dc.date.issued |
2009 |
|
| dc.identifier.citation |
57-68 |
vi |
| dc.identifier.issn |
0866-8612 |
|
| dc.identifier.uri |
http://tainguyenso.vnu.edu.vn/jspui/handle/123456789/11960 |
|
| dc.description.abstract |
Let $\mu$ be the $m-$fold convolution of the standard Cantor measure and $\underline{\alpha}_m$ be the lower extreme value of the local dimension of the measure $\mu$. The values of $\underline{\alpha}_m$ for $m=2,3,4$ were showed in [4] and [5]. In this paper, we show that $$\underline{\alpha}_5=|\frac{\log \big[\frac{2}{3.2^5}\big(\sqrt{145}\cos(\frac{\arccos\frac{427}{59\sqrt{145}}}{3})+5\big)\big]}{\log 3}|\approx 0.972638.$$
This values was estimated by P. Shmerkin in [5], but it has not been proved. |
vi |
| dc.language.iso |
en |
vi |
| dc.publisher |
Tap chi Khoa hoc |
vi |
| dc.subject |
Local dimension, probability measure, standard Cantor measure. |
vi |
| dc.title |
The extreme value of local dimension of convolution of the cantor measure |
vi |
| dc.type |
Article |
vi |