Cantor type functions in non-integer bases
Claudio Baiocchi, Vilmos Komornik, Paola Loreti
TL;DR
This paper explores generalized Cantor functions in non-integer bases, examining their properties and behaviors, revealing both similarities and differences with the classical Cantor function.
Contribution
It introduces a broad class of base-change functions in non-integer bases and analyzes their properties, expanding understanding of fractal and measure-theoretic behaviors.
Findings
Some functions share Cantor's function properties
Others exhibit distinct behaviors in non-integer bases
The study broadens the scope of fractal function analysis
Abstract
Cantor's ternary function is generalized to arbitrary base-change functions in non-integer bases. Some of them share the curious properties of Cantor's function, while others behave quite differently.
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