Vol. 5, No. 2, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18, 1 issue

Volume 17, 10 issues

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
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