Ланцюгове $D_2$-зображення дійсних чисел і деякі функції, з ним пов'язані
The properties of the representation of real numbers by continued fractions whose elements are equal to 0 and 1 (Denjoy's continued fractions) are studied.The geometry of this representation (properties of cylindrical sets, geometric content of digits, etc.) is investigated.Two projectors o...
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| Дата: | 2019 |
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| Автори та афіліації: |
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| Ключові слова: | keywords |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Інститут математики НАН України
2019
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| Онлайн доступ: | https://trim.imath.kiev.ua/index.php/trim/article/view/451 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Репозитарії
Transactions of Institute of Mathematics of NAS of Ukraine| Резюме: | The properties of the representation of real numbers by continued fractions whose elements are equal to 0 and 1 (Denjoy's continued fractions) are studied.The geometry of this representation (properties of cylindrical sets, geometric content of digits, etc.) is investigated.Two projectors of $D_2$-continued fraction representation of numbers into classical binary and nega-binary representations are studied.%Namely, these are the functions whose argument $x$ is written in the $D_2$-continued fraction representation and the values of the function $y$ is written in another representation with the same digits.Functional equations that satisfy these functions are given.The Lebesgue measure and the Hausdorff-Bezikovich fractal dimension of their sets of values are calculated.For one of these functions an equivalent definition of the system of two functional equations is given. |
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