Caustics of Weakly Lagrangian Distributions

Seán Gomes*, Jared Wunsch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study semiclassical sequences of distributions uh associated with a Lagrangian submanifold of phase space L⊂ TX. If uh is a semiclassical Lagrangian distribution, which concentrates at a maximal rate on L, then the asymptotics of uh are well understood by work of Arnol’d, provided L projects to X with a stable simple Lagrangian singularity. We establish sup-norm estimates on uh under much more general hypotheses on the rate at which it is concentrating on L (again assuming a stable simple projection). These estimates apply to sequences of eigenfunctions of integrable and KAM Hamiltonians.

Original languageEnglish (US)
JournalAnnales Henri Poincare
StateAccepted/In press - 2021

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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