Caustics of Weakly Lagrangian Distributions
| Autor: | Jared Wunsch, Sean Gomes |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Nuclear and High Energy Physics Semiclassical physics Statistical and Nonlinear Physics Eigenfunction Submanifold Projection (relational algebra) Mathematics - Analysis of PDEs Distribution (mathematics) Singularity Simple (abstract algebra) Mathematics::Quantum Algebra Phase space FOS: Mathematics 58J40 35A23 58K35 Mathematics::Symplectic Geometry Mathematical Physics Analysis of PDEs (math.AP) Mathematical physics |
| Zdroj: | Annales Henri Poincaré. 23:1205-1237 |
| ISSN: | 1424-0661 1424-0637 |
| DOI: | 10.1007/s00023-021-01110-8 |
| Popis: | We study semiclassical sequences of distributions $u_h$ associated to a Lagrangian submanifold of phase space $\lag \subset T^*X$. If $u_h$ is a semiclassical Lagrangian distribution, which concentrates at a maximal rate on $\lag,$ then the asymptotics of $u_h$ are well-understood by work of Arnol'd, provided $\lag$ projects to $X$ with a stable Lagrangian singularity. We establish sup-norm estimates on $u_h$ under much more general hypotheses on the rate at which it is concentrating on $\lag$ (again assuming a stable projection). These estimates apply to sequences of eigenfunctions of integrable and KAM Hamiltonians. 33 pages, 3 tables, 1 figure |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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