Abstract
We study analogues of Minkowski’s question mark function ?(x) related to continued fractions with even or with 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.
Original language | English (US) |
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Pages (from-to) | 35-57 |
Number of pages | 23 |
Journal | Monatshefte fur Mathematik |
Volume | 187 |
Issue number | 1 |
DOIs | |
State | Published - Sep 1 2018 |
Keywords
- Even continued fraction
- Farey map
- Gauss map
- Hölder exponent
- Odd continued fraction
- Question mark function
ASJC Scopus subject areas
- General Mathematics