Geodesic
The relative Renyi dimention
Problemy analiza, Tome 1 (2012) no. 1, pp. 15-23.

Voir la notice de l'article provenant de la source Math-Net.Ru

Recently, many authors are discussing the use of methods of fractal geometry [5] to compare the distributions of the various measures. However, in practical applications, comparison of distributions by comparing the calculated multifractal spectra can be difficult. It often happens that a completely different distributions of measures can give very imperceptible differences in the spectra. To solve this problem, some authors [4,10] propose to use different methods of direct comparison of distributions. These methods are generalizations of the classical multifractal analysis developed in the works L. Olsen [9], K.-S. Lo and S.-M. Ngai [8] and others. Based on the idea of multifractal analysis [9] and the mutual multifractal analysis [1,2] we propose to introduce new concepts of relative Renyi dimensions for coverings, packings and partitions, as well as we establish some connection between them. It should be noted that these dimension proved mathematically rigorous new analogues «new relative multifractal spectrum of dimensions» proposed for purely practical purposes, R. Dansereau and W. Kinser [6]. 
@article{PA_2012_1_1_a1,
     author = {N. Yu. Svetova},
     title = {The relative {Renyi} dimention},
     journal = {Problemy analiza},
     pages = {15--23},
     publisher = {mathdoc},
     volume = {1},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PA_2012_1_1_a1/}
}
TY  - JOUR
AU  - N. Yu. Svetova
TI  - The relative Renyi dimention
JO  - Problemy analiza
PY  - 2012
SP  - 15
EP  - 23
VL  - 1
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2012_1_1_a1/
LA  - ru
ID  - PA_2012_1_1_a1
ER  - 
%0 Journal Article
%A N. Yu. Svetova
%T The relative Renyi dimention
%J Problemy analiza
%D 2012
%P 15-23
%V 1
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2012_1_1_a1/
%G ru
%F PA_2012_1_1_a1
N. Yu. Svetova. The relative Renyi dimention. Problemy analiza, Tome 1 (2012) no. 1, pp. 15-23. http://geodesic.mathdoc.fr/item/PA_2012_1_1_a1/

[1] Svetova N. Yu., “Vzaimnye multifraktalnye spektry I. Tochnye spektry”, Trudy Petrozavodskogo gosudarstvennogo universiteta. Ser. Matematika, 2004, no. 11, 42–47, Izd-vo PetrGU, Petrozavodsk | MR

[2] Svetova N. Yu., “Vzaimnye multifraktalnye spektry II. Spektry Lezhandra, Khentshel–Prokachia i spektry, opredelennye dlya razbienii”, Trudy PetrGU. Ser. Matematika, 2004, no. 11, 47–56 | MR | Zbl

[3] Besicovich A. S., “A general form of the covering principle and relative differentiation of additive functions”, Proc. Cambridge Philos. Soc., 41 (1945), 103–110 | DOI | MR

[4] Cole J., “Relative multifractal analysis”, Chaos, solitons fractals, 2000, no. 11, 2233–2250 | DOI | MR | Zbl

[5] Falconer K. J., Fractal geometry. Mathematical Foundations and Applications, John Wiley Sons, New York, 1990, 337 pp. | MR | Zbl

[6] Dansereau R., Kinser W., “New relative multifractal dimension measures”, 26th International Conference on Acoustics, Speech and Signal Processing (ICASSP'2001) (Salt Lake City. Utah., May 7–11), 2001, 4

[7] Lanterman A. D., O'Sullivan J. A., Miller M. I., “Kullback-Leibler distances for quatifying clutter and models”, Optical engineering, 38:2 (1999), 2134–2146

[8] Lau K.-S., Ngai S.-M., “Multifractal measures and a weak separation condition”, Advances in mathematics, 1999, no. 141, 45–96 | DOI | MR | Zbl

[9] Olsen L., “A multifractal formalism”, Advances in mathematics, 1995, no. 116, 82–195 | DOI | MR

[10] Riedi R. H., Scheuring I., “Conditional and relative multifractal spectra”, Fractals, 5:1 (1997), 153–168 | DOI | MR | Zbl