On Minkowski type question mark functions associated with even or odd continued fractions

Abstract

We study analogues of Minkowski's question mark function $?(x)$ related to continued fractions with even or odd partial quotients. We prove that these functions are Hölder continuous with precise exponents, and that they linearize the appropriate versions of the Gauss and Farey maps.

17 pages; updated version

References in corpus (2)

• Fractal analysis for sets of non-differentiability of Minkowski's question mark function
• Orthogonal polynomials for Minkowski's question mark function

Cited by in corpus (2)

• $\alpha$-Expansions with odd partial quotients
• Slow continued fractions and permutative representations of ${\mathcal{O}}_N$