Propagation of well-prepared states along Martinet singular geodesics

Yves Colin de Verdière (1) , Cyril Letrouit (2, 3, 4)

1 IF - Institut Fourier
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 CaGE - Control And GEometry
4 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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.

Domaines: Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Yves Colin de Verdière, Cyril Letrouit. Propagation of well-prepared states along Martinet singular geodesics. Journal of Spectral Theory, 2022, 12, pp.1235-1253. ⟨10.48550/arXiv.2105.03305⟩. ⟨hal-03220110v2⟩