## The Brjuno functions and their regularity properties.(English)Zbl 0947.30018

Authors’ abstract: We show that various possible versions of the Brjuno functions, based on different kinds of continued fraction developments, are all equivalent, and we study their regularity ($$L^p$$, BMO (= bounded mean oscillation and Hölder) properties through a systematic analysis of the functional equation which they fulfill”.

### MSC:

 30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable 37B99 Topological dynamics 11A55 Continued fractions 30B70 Continued fractions; complex-analytic aspects 37F99 Dynamical systems over complex numbers

### Keywords:

Brjuno functions; continued fraction; regularity
Full Text: