The mutual singularity of multifractal measures for some non-regular Moran fractals

• Autorzy: Selmi Bilel

Identyfikatory

DOI

10.4064/ba210216-9-10

• Języki publikacji: EN

Abstrakty

EN

We study the multifractal dimension functions of the Moran measure associated with a homogeneous (non-regular) Moran fractal and show that the multifractal measures are mutually singular when the multifractal Hausdorff and packing functions differ. As an application, we give concrete examples related to these concepts.

Słowa kluczowe

EN

multifractal analysis; homogeneous Moran fractals; homogeneous Moran measures

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2021
• Tom: Vol. 69, no. 1
• Strony: 21--35
• Opis fizyczny: Bibliogr. 21 poz., wykr.

Twórcy

autor

Selmi Bilel

• Analysis, Probability & Fractals Laboratory LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir, 5000 Monastir, Tunisia

• https://orcid.org/0000-0001-8823-6699

Bibliografia

• [1] N. Attia and B. Selmi, Regularities of multifractal Hewitt-Stromberg measures, Comm. Korean Math. Soc. 34 (2019), 213-230.
• [2] N. Attia and B. Selmi, A multifractal formalism for Hewitt-Stromberg measures, J. Geom. Anal. 31 (2021), 825-862.
• [3] N. Attia and B. Selmi, On the mutual singularity of Hewitt-Stromberg measures, Analysis Math. 47 (2021), 273-283.
• [4] F. Ben Nasr, I. Bhouri and Y. Heurteaux, The validity of the multifractal formalism: results and examples, Adv. Math. 165 (2002), 264-284.
• [5] F. Ben Nasr and J. Peyrière, Revisiting the multifractal analysis of measures, Rev. Mat. Iberoamer. 29 (2013), 315-328.
• [6] M. Das, Hausdorff measures, dimensions and mutual singularity, Trans. Amer. Math. Soc. 357 (2005), 4249-4268.
• [7] Z. Douzi and B. Selmi, On the mutual singularity of multifractal measures, Electron. Res. Arch. 28 (2020), 423-432.
• [8] Z. Douzi and B. Selmi, The mutual singularity of the relative multifractal measures, Nonautonom. Dynam. Systems 8 (2021), 18-26.
• [9] Z. Douzi and B. Selmi, On the mutual singularity of Hewitt-Stromberg measures for which the multifractal functions do not necessarily coincide, Ricerche Mat. (online, 2021).
• [10] Z. Douzi, A. Samti and B. Selmi, Another example of the mutual singularity of multifractal measures, Proyecciones 40 (2021), 17-33.
• [11] L. Huang, Q. Liu and G. Wang, Multifractal analysis of Bernoulli measures on a class of homogeneous Cantor sets, J. Math. Anal. Appl. 491 (2020), art. 124362, 15 pp.
• [12] L. Olsen, A multifractal formalism, Adv. Math. 116 (1995), 82-196.
• [13] B. Selmi, Remarks on the mutual singularity of multifractal measures, Proyecciones 40 (2021), 71-82.
• [14] B. Selmi, Some new characterizations of Olsen’s multifractal functions, Results Math. 75 (2020), art. 147, 16 pp.
• [15] B. Selmi, The relative multifractal analysis, review and examples, Acta Sci. Math. 86 (2020), 635-666.
• [16] S. Shen, Multifractal analysis of some inhomogeneous multinomial measures with distinct analytic Olsen’s b and B functions, J. Statist. Phys. 159 (2015), 1216-1235.
• [17] M. Wu, The multifractal spectrum of some Moran measures, Sci. China Ser. A Math. 48 (2005), 97-112.
• [18] M. Wu, The singularity spectrum f(α) of some Moran fractals, Monatsh. Math. 144 (2005), 141-55.
• [19] M. Wu and J. Xiao, The singularity spectrum of some non-regularity Moran fractals, Chaos Solitons Fractals 44 (2011), 548-557.
• [20] J. Xiao and M. Wu, The multifractal dimension functions of homogeneous Moran measure, Fractals 16 (2008), 175-185.
• [21] Z. Yuan, Multifractal spectra of Moran measures without local dimension, Nonlinearity 32 (2019), 5060-5086.