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”.


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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