Лекція про мультифрактальність / Lecture on multifractality

Abstract: У лекції буде зроблено огляд різних підходів до мультифрактальності з прикладами. Буде представлено мультифрактальні добутки випадкових процесів і випадкових полів з деякими подробицями і сценаріями. Доповідь ґрунтується на спільних роботах [1–10].

This lecture presents is a survey of different approaches to multifractality with examples. The multifractal products of stochastic processes and random fields is presented with some details and scenarios. The talk is based on the joint papers [1–10].

[1] Leonenko, N.N., Nanayakkara, R., and Olenko, A. (2020). arXiv:2004.14522.
[2] Grahovac, D. and Leonenko, N.N. (2018). Fractals, 26(4), 1850055, 21 pp.
[3] Denisov, D. and Leonenko, N. (2016). Bernoulli, 22(4), 2579–2608.
[4] Denisov, D.E. and Leonenko, N.N. (2016). Stoch. Anal. Appl., 34(4), 610–643.
[5] Grahovac, D. and Leonenko, N.N. (2014). Chaos Solitons Fractals, 65, 78–89.
[6] Leonenko, N.N. and Shieh, N.-R. (2013). Fractals, 21(2), 1350009, 13 pp.
[7] Anh, V.V., Leonenko, N.N., Shieh, N.-R., and Taufer, E. (2010). Nonlinearity, 23(4), 823–843.
[8] Anh, V.V., Leonenko, N.N., and Shieh, N.-R. (2009). Bernoulli, 15(2), 508–531.
[9] Anh, V.V., Leonenko, N.N., and Shieh, N.-R. (2008). Adv. in Appl. Probab., 40(4), 1129–1156.
[10] Anh, V.V., Leonenko, N.N., and Shieh, N.-R. (2009). Stoch. Anal. Appl., 27(3), 475–499.

Ukrainianprobability

Audience: advanced learners

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Семінар з фрактального аналізу / Fractal analysis seminar

Series comments: Weekly research seminar on fractal analysis (online)

Topics:

• theory of fractals (fractal geometry and fractal analysis)
• Hausdorff–Besicovitch dimension, techniques and methods for its calculation and estimation
• functions and transformations preserving fractal (Hausdorff–Besicovitch, entropic, box-counting, packing, etc.) dimension
• sets of metric spaces that are essential for functions, sets, and dynamical systems
• self-similar, self-affine properties of mathematical objects
• systems of encoding for real numbers (numeral systems) and their applications
• metric number theory and metric theory of representations of numbers
• probabilistic number theory and probabilistic theory of representations of numbers
• measures supported on fractals, particularly singular measures and probability distributions
• nowhere monotonic and nowhere differentiable functions, functions with fractal properties
• theory of groups determined by invariants of transformations preserving tails of representation of numbers, digit frequencies, etc.

The talks are mostly in Ukrainian but English is also acceptable

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