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.

中文翻译：

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振荡积分和分形维数

我们研究具有解析相位函数和具有紧凑支撑的平滑振幅的振荡积分的几何表示。由振荡积分定义的曲线的几何特性取决于相位临界点的类型。我们为这些曲线的盒子尺寸和Minkowski含量给出了明确的公式。方法包括牛顿图和奇点解析。