46 citations · 126 across the 26 of their papers we have counts for
16 papers · 1 filter
Nonlinear chaotic Vlasov equations
Yann Chaubet, Daniel Han-Kwan, Gabriel Rivière
In this article, we study nonlinear Vlasov equations with a smooth interaction kernel on a compact manifold without boundary where the geodesic flow exhibits strong chaotic behavio…
Quantum limits of perturbed sub-Riemannian contact Laplacians in dimension 3
Victor Arnaiz, Gabriel Rivière
On the unit tangent bundle of a compact Riemannian surface, we consider a natural sub-Riemannian Laplacian associated with the canonical contact structure. In the large eigenvalue…
Length orthospectrum and the correlation function on flat tori
Nguyen Viet Dang, Matthieu Léautaud, Gabriel Rivière
This note presents some of the results obtained in arXiv:2207.05410 and it has beenthe object of a talk of the second author during the Journées "Équations auxDérivées Partielles"…
Length orthospectrum of convex bodies on flat tori
Nguyen Viet Dang, Matthieu Léautaud, Gabriel Rivière
In analogy with the study of Pollicott-Ruelle resonances on negatively curved manifolds, we define anisotropic Sobolev spaces that are well-adapted to the analysis of the geodesic…
Dynamics of nonlinear Klein-Gordon equations in low regularity on S^2
Joackim Bernier, Benoît Grébert, Gabriel Rivière
We describe the long time behavior of small non-smooth solutions to the nonlinear Klein-Gordon equations on the sphere S^2. More precisely, we prove that the low harmonic energies…
Local norms of Schr{ö}dinger eigenfunctions on
Gabriel Rivière
On the canonical -sphere and for Schr{ö}dinger eigenfunctions, we obtain a simple geometric criterion on the potential under which we can improve, near a given point and for eve…
Equidistribution of toral eigenfunctions along hypersurfaces
Hamid Hezari, Gabriel Riviere
We prove a new quantum variance estimate for toral eigenfunctions. As an application, we show that, given any orthonormal basis of toral eigenfunctions and any smooth embedded hype…
Two-microlocal regularity of quasimodes on the torus
Fabricio Macià, Gabriel Rivière
We study the regularity of stationary and time-dependent solutions to strong perturbations of the free Schrödinger equation on two-dimensional flat tori. This is achieved by perfor…
Observability and quantum limits for the Schrödinger equation on the sphere
Fabricio Macià, Gabriel Riviere
In this note, we describe our recent results on semiclassical measures for the Schr{ö}dinger evolution on Zoll manifolds. We focus on the particular case of eigenmodes of the Schr{…
Concentration and non-concentration for the Schrödinger evolution on Zoll manifolds
Fabricio Macià, Gabriel Rivière
We study the long time dynamics of the Schrödinger equation on Zoll manifolds. We establish criteria under which the solutions of the Schrödinger equation can or cannot concentrate…
Quantitative equidistribution properties of toral eigenfunctions
Hamid Hezari, Gabriel Riviere
We prove quantitative equidistribution properties for orthonormal bases of eigenfunctions of the Laplacian on the rational -torus. We show that the rate of equidistribution of s…
Long-time dynamics of the perturbed Schrödinger equation on negatively curved surfaces
Gabriel Riviere
We consider perturbations of the semiclassical Schr{ö}dinger equation on a compact Riemannian surface with constant negative curvature and without boundary. We show that, for scale…
norms, nodal sets, and quantum ergodicity
Hamid Hezari, Gabriel Riviere
For small range of , we improve the bounds of eigenfunctions of the Laplacian on negatively curved manifolds. Our improvement is by a power of logarithm for a full densi…
Perturbation of the semiclassical Schrödinger equation on negatively curved surfaces
Suresh Eswarathasan, Gabriel Riviere
We consider the semiclassical Schrödinger equation on a compact negatively curved surface. For any sequence of initial data microlocalized on the unit cotangent bundle, we look at…
Eigenmodes of the damped wave equation and small hyperbolic subsets
Gabriel Riviere, Stéphane Nonnenmacher
We study stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. In the high frequency limit, we prove that a sequence of …
Dispersion and controllability for the Schrödinger equation on negatively curved manifolds
Nalini Anantharaman, Gabriel Riviere
We study the time-dependent Schrödinger equation on a compact riemannian manifold on which the geodesic flow has the Anosov property.…