Asymptotic solutions: glancing trajectories, Lagrangian singularities, and Bessel cylinders
Abstract
We find a normal form for the simplest Lagrangian singularity appearing as the projection onto the space-energy of a solution to the Hamilton-Jacobi equation. Using this normal form we approximate asymptotic solutions of an equation (H-E0) \, uh = fh with a semiclassical distribution fh microlocalized on a Lagrangian manifold Λ0 when E0 is a critical value of the restriction H|Λ0.
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