Propagation of well-prepared states along Martinet singular geodesics

2021/05/07 by Yves Colin de Verdìère, Cyril Letrouit, de Verdière, Yves Colin +2 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2105.03305

openalex publication_date 2021/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/16

Abstract

We prove that for the Martinet wave equation with "flat" metric, which a subelliptic wave equation, singularities can propagate at any speed between 0 and 1 along any singular geodesic. This is in strong contrast with the usual propagation of singularities at speed 1 for wave equations with elliptic Laplacian.

Cited by

• Quantum limits of the Martinet sub-Laplacian

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