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arXiv · 2606.26962

Asymptotic solutions: glancing trajectories, Lagrangian singularities, and Bessel cylinders

Ilya Bogaevskii·Michel Rouleux
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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 $(\widehat{H}-E_0) \, u_h = f_h$ with a semiclassical distribution $f_h$ microlocalized on a Lagrangian manifold $\Lambda_0$ when $E_0$ is a critical value of the restriction $H|_{\Lambda_0}$.

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Ilya Bogaevskii, Michel Rouleux. 2026-06-25. Asymptotic solutions: glancing trajectories, Lagrangian singularities, and Bessel cylinders. https://arxiv.org/abs/2606.26962

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