# New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics

```@article{Dobrokhotov2013NewFF,
title={New formulas for Maslov’s canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics},
author={S. Yu. Dobrokhotov and George N. Makrakis and Vladimir Evgen'evich Nazaikinskii and T. Ya. Tudorovskii},
journal={Theoretical and Mathematical Physics},
year={2013},
volume={177},
pages={1579-1605}
}```
• Published 1 August 2013
• Mathematics
• Theoretical and Mathematical Physics
We suggest a new representation of Maslov’s canonical operator in a neighborhood of caustics using a special class of coordinate systems (eikonal coordinates) on Lagrangian manifolds. We present the results in the two-dimensional case and illustrate them with examples.
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Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid