Analysis & PDE

  • Anal. PDE
  • Volume 5, Number 2 (2012), 313-338.

Dispersion and controllability for the Schrödinger equation on negatively curved manifolds

Nalini Anantharaman and Gabriel Rivière

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We study the time-dependent Schrödinger equation ıut=12Δu, 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.

Article information

Anal. PDE, Volume 5, Number 2 (2012), 313-338.

Received: 28 July 2010
Revised: 27 August 2011
Accepted: 31 August 2011
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 35B37

Schrödinger equation semiclassical analysis control theory


Anantharaman, Nalini; Rivière, Gabriel. Dispersion and controllability for the Schrödinger equation on negatively curved manifolds. Anal. PDE 5 (2012), no. 2, 313--338. doi:10.2140/apde.2012.5.313.

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