The local limit problem and Hölder-continuity
✍ Scribed by Wolfgang Macht; Werner Wolf
- Publisher
- Springer
- Year
- 1989
- Tongue
- English
- Weight
- 482 KB
- Volume
- 82
- Category
- Article
- ISSN
- 1432-2064
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This work focuses on the local Hölder exponent as a measure of the regularity of a function around a given point. We investigate in detail the structure and the main properties of the local Hölder function (i.e., the function that associates to each point its local Hölder exponent). We prove that it
We prove that the semi-conjugacy, obtained by P. Arnoux (1988, Bull. Soc. Math. France 116, 489-500), between an interval exchange map and a translation on the torus is Hölder continuous and we compute the Hölder exponent. This semiconjugacy is a particular case of a space filling curve.