Renormalization of Quasiperiodic Mappings

This paper will focus on the connection between renormalization of dynamical systems with two frequencies and the discrete 1-D Schroedinger equation with an incommensurate modulation. The connection will be explored by constructing a renormalization group formulation of both problems using a binary "Farey" address to label the incommensurability. This address is closely related to the continued fraction representation which has previously been used to investigate these problems. The emphasis of this paper is to introduce a new method rather than to present a completed calculation. Future investigations will determine whether this will eventually lead to deeper insights into these problems than can be obtained using the continued fractions.