On the Information Dimensions

Józef Myjak; Ryszard Rudnicki

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 2, page 357-364
  • ISSN: 0392-4033

Abstract

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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

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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

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  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
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  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

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