Diophantine conditions and real or complex Brjuno functions

P. Moussa, S. Marmi

The continued fraction expansion of the real number $x=a_0+x_0, a_0\in {\ZZ},$ is given by $0\leq x_n<1, x_{n}^{-1}=a_{n+1}+ x_{n+1}, a_{n+1}\in {\NN},$ for $n\ge 0.$ The Brjuno f…