A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.
Si studiano i legami fra la dimensione informatica (information dimension) e la dimensione media (average dimension) della misura. Inoltre si dimostra che la dimensione media è positivamente lineare e continua rispetto della norma supremum nello spazio delle misure.
@article{BUMI_2007_8_10B_2_357_0,
author = {J\'ozef Myjak and Ryszard Rudnicki},
title = {On the Information Dimensions},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {10-A},
year = {2007},
pages = {357-364},
zbl = {1178.28003},
mrnumber = {2339446},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_2_357_0}
}
Myjak, Józef; Rudnicki, Ryszard. On the Information Dimensions. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 357-364. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_2_357_0/
[1] - , Random self-similar multifractals, Math. Nachr., 181 (1996), 5-42. | MR 1409071 | Zbl 0873.28003
[2] , Some results on the behavior and estimation of the fractal dimensions of distribution on attractors, J. Statist. Phys., 62 (1991), 651-708. | MR 1105278 | Zbl 0738.58029
[3] - , Measure Theory and Finite Properties of Functions, CRC Press Boca Raton, 1992. | MR 1158660 | Zbl 0804.28001
[4] Techniques in Fractal Geometry, Wiley, Chichester, 1997. | MR 1449135 | Zbl 0869.28003
[5] - , Coincidence of various dimensions associated with metrics and measures on metric spaces, Discrete Contin. Dynam. Systems, 3 (1997), 591-603. | MR 1465128 | Zbl 0948.37014
[6] - , The infinite number of generalized dimensions of fractals and strange attractors, Phys. D, 8 (1983), 435-444. | MR 719636 | Zbl 0538.58026
[7] - , Chaos, Fractals and Noise. Stochastic Aspects of Dynamics. Springer Applied Mathematical Sciences, 97, New York, 1994. | MR 1244104
[8] , A multifractal formalism, Adv. in Math., 116 (1995), 82-196. | MR 1361481 | Zbl 0841.28012
[9] , Dimension Theory in Dynamical Systems. Contemporary views and applicationsUniversity of Chicago Press, Chicago, 1997, | MR 1489237
[10] , On rigorous mathematical definitions of correlation dimension and generalized spectrum for dimensions, J. Stat. Physics, 71 (1993), 529-547. | MR 1219021 | Zbl 0916.28006
[11] - , Continuous Markov semigroups and stability of transport equations, J. Math. Anal. Appl., 249 (2000), 668-685. | MR 1781248 | Zbl 0965.47026
[12] - - , On the characterization of chaotic motions, in Dynamical systems and chaos (Sitges/Barcelona, 1982), Lecture Notes in Phys., 179 Springer Berlin (1983), 212-222.
[13] , An improved multifractal formalism and self-similar measures, J. Math. Anal. Appl., 189 (1995), 462-490. | MR 1312056 | Zbl 0819.28008
[14] , Dimension, entropy and Lyapunov exponents, Ergodic Theory Dynam. Systems, 2 (1982), 109-124. | MR 684248