Фрактальні властивості множин та функцій, пов'язаних з марковським зображенням дійсних чисел, визначеним двічі стохастичною матрицею
We consider Markov representations of real numbers from $[0,1]$ defined by doubly-stochastic matrices.These representation are enco\-dings of reals via binary alphabet.Topological, metric and fractal properties of real number sets with restrictions on usages of symbols in the Markov representation a...
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| Date: | 2017 |
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| Keywords: | keywords |
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| Format: | Article |
| Language: | Ukrainian |
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Інститут математики НАН України
2017
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/403 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | We consider Markov representations of real numbers from $[0,1]$ defined by doubly-stochastic matrices.These representation are enco\-dings of reals via binary alphabet.Topological, metric and fractal properties of real number sets with restrictions on usages of symbols in the Markov representation are described.Properties of a function associated to a real number $x$ with a Markov representation $\Delta^{M}_{\alpha_1 \alpha_2 \ldots \alpha_n \ldots}$ the number $MD(x)$ having binary representation $(\alpha_1 \alpha_2 \ldots \alpha_n \ldots)$ are investigated. |
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