Back to Search
Start Over
Caustics of weakly Lagrangian distributions
- Publication Year :
- 2020
-
Abstract
- 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.<br />Comment: 33 pages, 3 tables, 1 figure
- Subjects :
- Mathematics - Analysis of PDEs
58J40, 35A23, 58K35
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2001.10647
- Document Type :
- Working Paper