| Title:
|
On some properties of the metric dimension (English) |
| Author:
|
Mišík, Ladislav |
| Author:
|
Žáčik, Tibor |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1990 |
| Pages:
|
781-791 |
| . |
| Category:
|
math |
| . |
| MSC:
|
51K99 |
| MSC:
|
54D20 |
| MSC:
|
54F45 |
| idZBL:
|
Zbl 0717.54017 |
| idMR:
|
MR1091376 |
| . |
| Date available:
|
2008-06-05T21:46:30Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/106914 |
| . |
| Reference:
|
[B] Bakhtin V. I.: Properties of the entropy and Hausdorff dimension (in Russian).Vestnik Moskov. Univ. Ser. 1 Mat. Meh. 15 (1982), 25-29. MR 0679473 |
| Reference:
|
[BT] Besicovitch A. S., Taylor S. J.: On the complementary intervals of a linear closed sets of zero Lebesgue measure.L. London Math. Soc. 29 (1954), 449-459. MR 0064849 |
| Reference:
|
[CS] Cajar H., Sandan K.: Perfekte Mengen mit unterschiedlicher Hausdorff und unterer metrischer Dimension.Arch. Math. 45 (1985), 21-33. MR 0799446 |
| Reference:
|
[H] Hawkes J.: Hausdorff measure, entropy, and the independence of small sets.Proc. London Math. Soc. (3) 28 (1974), 700-724. Zbl 0315.28001, MR 0352412 |
| Reference:
|
[KT] Kolmogorov A. N., Tihomirov V. M.: e-entropy and e-capacity of sets in functional spaces (in Russian).Usp. Mat. Nauk 14 (1959), 3-86; Am. Math. Soc. Transl. IT (1961), 277-364. MR 0112032 |
| Reference:
|
[M] Maňé R.: On the dimension of the compact invariant sets of certain nonlinear maps."Dynamical Systems and Turbulence", Warwick 1980 (Coventry 1979/1980), Lecture Notes in Math. 898, Springer, Berlin - New York 1981, 230-242. MR 0654892 |
| Reference:
|
[P] Prosser R. T.: Note on metric dimension.Proc. Amer. Math. Soc. 25 (1970), 763-765. Zbl 0197.19303, MR 0259873 |
| Reference:
|
[PS] Pontryagin L. S., Snirelman L. G.: Sur une proprieie metrique de la dimension.Annals of Math. 33 (1932), 156-162. Appendix to the Russian translation of "Dimension Theory" by W. Hurewitcz and H. Wallman, Izdat. Inostr. Lit. Moscow, 1948. MR 1503042 |
| Reference:
|
[PT] Palis J., Takens F.: Hyperbolicity and the creation of homoclinic orbits.Annals of Mathematics 125 (1987), 337-374. Zbl 0641.58029, MR 0881272 |
| Reference:
|
[V] Vosburg A. C.: On the relationship between Hausdorff dimension and metric dimension.Pacific J. Math. 23 (1967), 183-187. Zbl 0153.24701, MR 0217776 |
| Reference:
|
[Y] Yomdin Y.: The geometry of critical and near-critical values of differentiable mappings.Math. Ann. 264 (1983), 495-515. Zbl 0507.57019, MR 0716263 |
| . |
