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We suggest a new representation of Maslov's canonical operator in aneighborhood of the caustics using a special class of coordinate systems("eikonal coordinates") on Lagrangian manifolds. The specific features of thetwo-dimensional case are considered. The general case is treated inarXiv:1307.2292 [math-ph].

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