Caustics of Weakly Lagrangian Distributions

We study semiclassical sequences of distributions \(u_h\) associated with a Lagrangian submanifold phase space \(\mathcal {L}\subset T^*X\). If is distribution, which concentrates at maximal rate on {L},\) then the asymptotics are well understood by work Arnol’d, provided {L}\) projects to X stable simple singularity. establish sup-norm estimates under much more general hypotheses it concentrating (again assuming projection). These apply eigenfunctions integrable and KAM Hamiltonians.