Spreading of Lagrangian regularity on rational invariant tori

Jared Wunsch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Let P h be a self-adjoint semiclassical pseudodifferential operator on a manifold M such that the bicharacteristic flow of the principal symbol on T*M is completely integrable and the subprincipal symbol of P h vanishes. Consider a semiclassical family of eigenfunctions, or, more generally, quasimodes u h of P h . We show that on a nondegenerate rational invariant torus, Lagrangian regularity of u h (regularity under test operators characteristic on the torus) propagates both along bicharacteristics, and also in an additional "diffractive" manner. In particular, in addition to propagating along null bicharacteristics, regularity fills in the interiors of small annular tubes of bicharacteristics.

Original languageEnglish (US)
Pages (from-to)487-496
Number of pages10
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - Apr 2008

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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