Renormalization group analysis of quasi-periodicity in analytic maps

Analytic maps of the form (f(z) = e^{2pi iOmega } z + mathcal{O}(z^2 )) display quasiperiodicity when Ω satisfies a diophantine condition. Quasiperiodic motion is confined to a neighborhood of the origin known as a Siegel domain. The boundary of this domain obeys universal scaling relations. In this paper we investigate these scaling relations through a renormalization group analysis, and we discuss singularities and asymptotic form of the scaling function.