Francesco CELLAROSI (Princeton University)
The Geometry of Trigonometric Sums and Dynamics

Abstract: In this talk we analyze the geometry of the curves generated by quadratic trigonometric sums. We will see how the approximate multi- scale structure is described dynamically in terms of a Gauss-like map preserving an infinite measure. This map is related to the continued fraction expansion with even partial quotients and has anomalous scaling properties of the corresponding Birkhoff sums.