[en] We investigate the fractal properties of the Brjuno-Yoccoz function Y associated with the
nearest integer continued fraction. Similar to the conventional Brjuno function B, the Hölder exponents are not meaningful for Y. It is appropriate to replace the L∞ norm with an Lp norm and thus employ regularity in terms of membership in the spaces introduced by Calderón and Zygmund. We establish that the fractal properties of Y mirror those of B :
the p-exponent at x is equal to the inverse of the irrationality exponent of x.
Disciplines :
Mathematics
Author, co-author :
Lamby, Thomas ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
Language :
English
Title :
Pointwise regularity of generalized Brjuno function
Publication date :
2023
Event name :
Workshop Continued fractions : multifractal and dynamical aspects - CIRM
