Tori Matthieu Measurements (2024)

1. Tori Matthieu - ReverbNation

8 feb 2023 · Abstract. This note presents some of the results obtained in [DLR22] and it has been the object of a talk of the second author during the ...

After five years of studying agronomy, it was time for Mathieu to get on his bike and discover the idyllic landscapes of rural France and Spain.
Mathieu Willard

5 nov 2023 · LENGTH ORTHOSPECTRUM OF CONVEX BODIES ON FLAT TORI. NGUYEN VIET DANG, MATTHIEU LÉAUTAUD, AND GABRIEL RIVI`ERE. Abstract. In analogy with the ...
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6 nov 2023 · ... and impact investments (2022/2170(INI)) Committee on Employment and Social Affairs Rapporteur: Sara Matthieu.
REPORT on job creation - the just transition and impact investments (2022/2170(INI)) Committee on Employment and Social Affairs Rapporteur: Sara Matthieu

Yannick Bonthonneau, Nguyen Viet Dang, Matthieu Léautaud, Gabriel Rivi`ere ... Look for crystalline measures carried by length spectras. ... Poincaré Series and ...

3 jun 2014 · ... measures}. They are obtained by performing a finer localization in phase space around each of these tori ... From: Matthieu Léautaud [view email]
We analyse the structure of semiclassical and microlocal Wigner measures for solutions to the linear Schrödinger equation on the disk, with Dirichlet boundary conditions. Our approach links the propagation of singularities beyond geometric optics with the completely integrable nature of the billiard in the disk. We prove a "structure theorem", expressing the restriction of the Wigner measures on each invariant torus in terms of {\em second-microlocal measures}. They are obtained by performing a finer localization in phase space around each of these tori, at the limit of the uncertainty principle, and are shown to propagate according to Heisenberg equations on the circle. Our construction yields as corollaries (a) that the disintegration of the Wigner measures is absolutely continuous in the angular variable, which is an expression of the dispersive properties of the equation; (b) an observability inequality, saying that the $L^2$-norm of a solution on any open subset intersecting the boundary (resp. the $L^2$-norm of the Neumann trace on any nonempty open set of the boundary) controls its full $L^2$-norm (resp. $H^1$-norm). These results show in particular that the energy of solutions cannot concentrate on periodic trajectories of the billiard flow other than the boundary.