Cantor type functions in non-integer bases

Abstract

Cantor's ternary function is generalized to arbitrary basechange functions in non-integer bases. Some of them share the curious properties of Cantor's function, while others behave quite differently.Date: Version of 2016-05-04-a. 1 We apply the notations of symbolic dynamics, i.e, d ∞ denotes the constant sequence d, d, . . . , and 10 ∞ denotes the sequence 1, 0, 0, . . . .