# Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

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1 LM-Orsay - Laboratoire de Mathématiques d-Orsay 2 CMLS - Centre de Mathématiques Laurent Schwartz

Abstract : We study the time-dependent Schrödinger equation $\imath\frac{\partial u}{\partial t}=-\frac{1}{2}\Delta u,$ on a compact riemannian manifold on which the geodesic flow has the Anosov property. Using the notion of semiclassical measures, we prove various results related to the dispersive properties of the Schrödinger propagator, and to controllability.

Autor: Nalini Anantharaman - Gabriel Riviere -

Fuente: https://hal.archives-ouvertes.fr/

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