Geodesic
On the Mutual multifractal analysis for some non-regular Moran measures
Problemy analiza, Tome 12 (2023) no. 1, pp. 46-71.

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In this paper, we study the mutual multifractal Hausdorff dimension and the packing dimension of level sets $K(\alpha, \beta)$ for some non-regular Moran measures satisfying the so-called Strong Separation Condition. We obtain sufficient conditions for the valid multifractal formalisms of such measures and discuss examples.
Keywords: Moran sets, non-regular Moran measures.
Mots-clés : fractal/multifractal dimensions 
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B. Selmi; N. Yu. Svetova. On the Mutual multifractal analysis for some non-regular Moran measures. Problemy analiza, Tome 12 (2023) no. 1, pp. 46-71. http://geodesic.mathdoc.fr/item/PA_2023_12_1_a3/

[1] Aouidi J., Ben Mabrouk A., “A wavelet multifractal formalism for simultaneous singularities of functions”, Int. J. Wavelets Multiresolut. Inf. Process, 12:1 (2014), 14 pp. | DOI | MR | Zbl

[2] Arfaoui S., Ben Mabrouk A., Cattani C., Fractal analysis basic concepts and applications, Series On Advances In Mathematics For Applied Sciences, Worldscinet, 2022 | DOI | MR | Zbl

[3] Barreira L., Saussol B., “Variational principles and mixed multifractal spectra”, Trans. Amer. Math. Soc., 353 (2001), 3919–3944 | DOI | MR | Zbl

[4] Ben Mabrouk A., Ben Slimane M., Aouidi J., “Mixed multifractal analysis for functions: general upper bound and optimal results for vectors of self-similar or quasi-self-similar of functions and their superpositions”, Fractals, 24:4 (2016), 1650039, 12 pp. | DOI | MR | Zbl

[5] Ben Mabrouk A., Farhat A., “A mixed multifractal analysis for quasi-ahlfors vector-valued measures”, Fractals, 30:1 (2022), 2240001, 20 pp. | DOI | Zbl

[6] Ben Mabrouk A., Selmi B., “On the equivalence of multifractal measures on Moran sets”, Filomat, 36:10 (2022), 3483–3494 | DOI | MR

[7] Cawely R. G., Mauldin R. D., “Multifractal decompositions of Moran fractals”, Advances in Math., 92 (1992), 196–236 | DOI | MR

[8] Douzi Z., Selmi B., “Projections of mutual multifractal functions”, J. Class. Anal., 19 (2022), 21–37 | DOI | MR

[9] Douzi Z., Selmi B., “On the projections of the mutual multifractal Rényi dimensions”, Anal. Theory Appl., 37 (2021), 572–592 | DOI | MR | Zbl

[10] Douzi Z., Selmi B., Ben Mabrouk A., “The refined multifractal formalism of some homogeneous Moran measures”, Eur. Phys. J. Spec. Top., 230 (2021), 3815–3834 | DOI

[11] Fernbndez-Martnnez M., “A survey on fractal dimension for fractal structures”, Applied Mathematics and Nonlinear Sciences, 1 (2019), 437–472 | DOI | MR

[12] Gan G., Ma C., Wu J., Data Clustering Theory, Algorithms, and Applications, ASA-SIAM Series on Statistics, and Applied Probability, 2007 | DOI | MR | Zbl

[13] Hong L., Tie Y., Lanlan W., “Network traffic prediction based on multifractal MLD model”, International Workshop on Chaos-Fractal Theory and its Applications (Kunming, China, 2010), 2010, 466–470 | DOI

[14] Liu R., Lux T., “Non-homogeneous volatility correlations in the bivariate multifractal model”, Eur. J. Fin., 21 (2015), 971–991 | DOI

[15] Liu R., Lux T., “Generalized method of moment estimation of multivariate multifractal models”, Econ. Model., 67 (2017), 136–148 | DOI

[16] Olsen L., “A multifractal formalism”, Adv. Math., 116 (1995), 82–195 | DOI | MR

[17] Olsen L., “Mixed divergence points of self-similar measures”, Indiana Univ. Math. J., 52 (2003), 1343–1372 | DOI | MR | Zbl

[18] Olsen L., “Mixed generalized dimensions of self-similar measures”, J. Math. Anal. Appl., 306 (2005), 516–539 | DOI | MR | Zbl

[19] Olsen L., “On the inverse multifractal formalism”, Glasgow Mathematical Journal, 52 (2010), 179–194 | DOI | MR | Zbl

[20] Reznikov N., Bilton M., Lari L., Stevens M. M., Kröge R., “Fractal-like hierarchical organization of bone begins at the nanoscale”, Science, 360:6388 (2018) | DOI

[21] Selmi B., Ben Mabrouk A., “On the mixed multifractal formalism for vector-valued measures”, Proyecciones, 41 (2022), 1015–1032 | DOI | MR

[22] Selmi B., Svetova N., “On the projections of mutual $L^{q,t}$-spectrum”, Probl. Anal. Issues Anal., 6(24):2 (2017), 94–108 | DOI | MR | Zbl

[23] Svetova N., Mutual multifractal analysis. Application to the parameterization of mineral structures, Ph.D Thesis, Petrozavodsk, 2004

[24] Svetova N., “An estimate for exact mutual multifractal spectra”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 14 (2008), 59–66 | MR

[25] Svetova N., “The property of convexity of mutual multifractal dimension”, Tr. Petrozavodsk. Gos. Univ. Ser. Mat., 17 (2010), 15–24 | MR

[26] Slimane M., “Baire typical results for mixed Hölder spectra on product of continuous besov or oscillation spaces”, Mediterr. J. Math., 13 (2016), 1513–1533 | DOI | MR | Zbl

[27] Wen S., Wu M., “Relations between multifractal packing premeasure and measure on metric space”, Acta Math. Sci., 27 (2007), 137–144 | DOI | MR | Zbl

[28] Wen Z., “Moran sets and Moran classes”, Chinese Science Bulletin, 46 (2001), 1849–1856 | DOI | MR

[29] Wu M., “The singularity spectrum $f(\alpha)$ of some Moran fractals”, Monatsh. Math., 144 (2005), 141–155 | DOI | MR | Zbl

[30] Wu M., Xiao J., “The singularity spectrum of some non-regularity moran fractals”, Chaos Solitons Fractals, 44 (2011), 548–557 | DOI | MR | Zbl

[31] Xiao J., Wu M., “The multifractal dimension functions of homogeneous Moran measure”, Fractals, 16 (2008), 175–185 | DOI | MR | Zbl