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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
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