Oscillatory Integrals and Fractal Dimension
  We study geometrical representation of oscillatory integrals with an analytic phase function and a smooth amplitude with compact support. Geometrical properties of the curves defined by the oscillatory integral depend on the type of a critical point of the phase. We give explicit formulas for the box dimension and the Minkowski content of these curves. Methods include Newton diagrams and the resolution of singularities. 
Jean-Philippe Rolin, Domagoj Vlah, Vesna Zupanovic
math.CA