Ланцюгове $D_2$-зображення дійсних чисел і деякі функції, з ним пов'язані

Abstract

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.