... collide with the points of Xn−1(α). In terms of logarithms of conformal radii, this implies that theremust be a decrease of −1qnlog |α − pn/qn|. The theory of continued fractionsapproximates ... dynamical plane of Pp/q, the rays Rp/q(θ), θ ∈ Θ, form a periodic cycle of rays which land at 0.THE BRJUNO FUNCTION AND THE SIZE OF SIEGEL DISKS 281If p/q ∈ Z, the dynamical ray of argument ... qnqn,Annals of Mathematics The Brjuno function continuously estimates the size of quadratic Siegel disks By Xavier Buff and Arnaud Ch´eritat THE BRJUNO FUNCTION AND THE SIZE OF SIEGEL DISKS 283where...