A.S. Kryukovsky, D.S. Lukin, D.V. Rastyagaev
The purpose of the present work is the development of the theory of calculation of the main member of an oscillating integral asymptotic in a vicinity of a degenerate critical point of a phase on manifold with edge through the Newton’s diagram of a phase in a vicinity of this critical point. It is known, that this main member is determined by a point of crossing of the Newton’s diagram with a diagonal of the coordinate octant. Under these conditions the arithmetic progressions, which possess parameters of all members of asymptotic expansions, depend on the Newton’s diagram of a phase function. In the given work the structure of these progressions in the terms of the Newton’s diagram is considered. In the work the parameters of the main members of asymptotic expansions for phase functions appropriate to two-dimensional edge and corner wave catastrophes are calculated.