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

Marmi, S.; Moussa, P.; Yoccoz, J.-C.

Commun. Math. Phys. 186, No. 2, 265-293 (1997).

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”.

Reviewer: Tibor Šalát (Bratislava)

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