New formulas for Maslovs canonical operator in a neighborhood of focal points and caustics in 2D semiclassical asymptotics

We suggest a new representation of Maslovs canonical operator in a neighborhood of the caustics using a special class of coordinate systems (eikonal coordinates) on Lagrangian manifolds. The specific features of the two-dimensional case are considered. The general case is treated in arXiv:1307.2292 [math-ph].