Abstract
We introduce and study a continuous function I which is called a digit inversor for the Q 3-representation of the fractional part of a real number. This representation is determined by a probability vector.(q 0; q 1; q 2) with positive coordinates, generalizes the classical ternary representation, and coincides with this representation for q 0 = q 1 = q 2 = 1/3: The values of this function are obtained from the Q 3-representation of the argument by the following change of digits: 0 by 2; 1 by 1; and 2 by 0: The differential, integral, and fractal properties of the inversor are described. We prove that I is a singular function for q 0 ≠ q 2.
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