Marmi, S.; Moussa, P.; Yoccoz, J.-C. The Brjuno functions and their regularity properties. (English) Zbl 0947.30018 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) Cited in 4 ReviewsCited in 47 Documents 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 PDF BibTeX XML Cite \textit{S. Marmi} et al., Commun. Math. Phys. 186, No. 2, 265--293 (1997; Zbl 0947.30018) Full Text: DOI OpenURL