Vol. 5, No. 2, 2012

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ISSN: 1948-206X (e-only)
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Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

Nalini Anantharaman and Gabriel Rivière

Vol. 5 (2012), No. 2, 313–338
Abstract

We study the time-dependent Schrödinger equation ıu t = 1 2Δu, 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.

Keywords
Schrödinger equation, semiclassical analysis, control theory
Mathematical Subject Classification 2000
Primary: 35B37
Milestones
Received: 28 July 2010
Revised: 27 August 2011
Accepted: 31 August 2011
Published: 27 August 2012
Authors
Nalini Anantharaman
Laboratoire de Mathématiques (UMR 8628)
Université Paris-Sud XI
Bâtiment 425
91405 Orsay Cedex
France
Gabriel Rivière
Laboratoire Paul Painlevé (UMR 8524)
Université Lille 1
Bâtiment M3
59655 Villeneuve d’Ascq Cedex
France