Brjuno number

Summary

A Brjuno number is an irrational number whose continued fraction convergents have denominators that do not grow too fast. The condition is that the series $\sum_n \log(q_{n+1}) / q_n$ converges. Brjuno numbers are exactly the rotation numbers for which every holomorphic germ with that rotation at a fixed point can be linearized. They are central to small divisor problems and to the existence of Siegel discs.