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

## TL;DR

This paper investigates Minkowski-type question mark functions linked to even and odd continued fractions, establishing their Hölder continuity and their role in linearizing specific Gauss and Farey maps.

## Contribution

It introduces new Minkowski-type functions for even and odd continued fractions and proves their Hölder continuity and their linearizing properties for related dynamical systems.

## Key findings

- Functions are Hölder continuous with explicit exponents
- They linearize the associated Gauss and Farey maps
- New connections between continued fractions and dynamical systems

## 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 H\"older continuous with precise exponents, and that they linearize the appropriate versions of the Gauss and Farey maps.