On the Information Dimensions

Józef Myjak; Ryszard Rudnicki

Bollettino dell'Unione Matematica Italiana (2007)

• Volume: 10-B, Issue: 2, page 357-364
• ISSN: 0392-4041

Access Full Article

top

 Access to full text

 Full (PDF)

 Full (DjVu)

Abstract

top

A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.

How to cite

top

• MLA
• BibTeX
• RIS

Myjak, Józef, and Rudnicki, Ryszard. "On the Information Dimensions." Bollettino dell'Unione Matematica Italiana 10-B.2 (2007): 357-364. <http://eudml.org/doc/290414>.

@article{Myjak2007,
abstract = {A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.},
author = {Myjak, Józef, Rudnicki, Ryszard},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {357-364},
publisher = {Unione Matematica Italiana},
title = {On the Information Dimensions},
url = {http://eudml.org/doc/290414},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Myjak, Józef
AU - Rudnicki, Ryszard
TI - On the Information Dimensions
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/6//
PB - Unione Matematica Italiana
VL - 10-B
IS - 2
SP - 357
EP - 364
AB - A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.
LA - eng
UR - http://eudml.org/doc/290414
ER -

References

top

1. ARBEITER, M. - PATZSCHKE, N., Random self-similar multifractals, Math. Nachr., 181 (1996), 5-42. Zbl0873.28003MR1409071DOI10.1002/mana.3211810102
2. CUTLER, C. D., Some results on the behavior and estimation of the fractal dimensions of distribution on attractors, J. Statist. Phys., 62 (1991), 651-708. Zbl0738.58029MR1105278DOI10.1007/BF01017978
3. EVANS, L. C. - GARIEPY, R. F., Measure Theory and Finite Properties of Functions, CRC PressBoca Raton, 1992. Zbl0804.28001MR1158660
4. FALCONER, K. J.Techniques in Fractal Geometry, Wiley, Chichester, 1997. Zbl0869.28003MR1449135
5. GUYSINSKY, M. - YASKOLKO, S., Coincidence of various dimensions associated with metrics and measures on metric spaces, Discrete Contin. Dynam. Systems, 3 (1997), 591-603. Zbl0948.37014MR1465128DOI10.3934/dcds.1997.3.591
6. HENTSCHEL, H. - PROCACCIA, I., The infinite number of generalized dimensions of fractals and strange attractors, Phys. D, 8 (1983), 435-444. Zbl0538.58026MR719636DOI10.1016/0167-2789(83)90235-X
7. LASOTA, A. - MACKEY, M. C., Chaos, Fractals and Noise. Stochastic Aspects of Dynamics. Springer Applied Mathematical Sciences, 97, New York, 1994. MR1244104DOI10.1007/978-1-4612-4286-4
8. OLSEN, L., A multifractal formalism, Adv. in Math., 116 (1995), 82-196. Zbl0841.28012MR1361481DOI10.1006/aima.1995.1066
9. PESIN, Y. B., Dimension Theory in Dynamical Systems. Contemporary views and applicationsUniversity of Chicago Press, Chicago, 1997, MR1489237DOI10.7208/chicago/9780226662237.001.0001
10. PESIN, Y. B., On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions, J. Stat. Physics, 71 (1993), 529-547. Zbl0916.28006MR1219021DOI10.1007/BF01058436
11. PICHÓR, K. - RUDNICKI, R., Continuous Markov semigroups and stability of transport equations, J. Math. Anal. Appl., 249 (2000), 668-685. Zbl0965.47026MR1781248DOI10.1006/jmaa.2000.6968
12. PROCACCIA, I. - GRASSBERGER, P. - HENTSCHEL, H. G. E., On the characterization of chaotic motions, in Dynamical systems and chaos (Sitges/Barcelona, 1982), Lecture Notes in Phys., 179SpringerBerlin (1983), 212-222. 
13. RIEDI, R., An improved multifractal formalism and self-similar measures, J. Math. Anal. Appl., 189 (1995), 462-490. Zbl0819.28008MR1312056DOI10.1006/jmaa.1995.1030
14. YOUNG, L.-S., Dimension, entropy and Lyapunov exponents, Ergodic Theory Dynam. Systems, 2 (1982), 109-124. MR684248

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.

Language to use for this widget. български (bg) čeština (cs) Deutsch (de) ελληνικά (el) English (en) español (es) français (fr) italiano (it) lietuvių kalba (lt) polski (pl) português (pt) română (ro) русский (ru) slovenčina (sk)

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

Number of notes per page 5 10 15 20

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.

OK