Titre :

Delocalization of slowly damped eigenmodes on Anosov manifolds

Auteur(s) :

Riviere, Gabriel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Communications in Mathematical Physics

Pagination :

555-593

Éditeur :

Springer Verlag

Date de publication :

2012-11-11

ISSN :

0010-3616

Mot(s)-clé(s) en anglais :

damped wave equation
semiclassical measures
Anosov flows
topological pressure
Kolmogorov-Sinai entropy

Discipline(s) HAL :

Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Systèmes dynamiques [math.DS]

Résumé en anglais : [en]

We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to ...
Lire la suite >We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with spectral parameters which are asymptotically close enough to the real axis. We prove that such modes cannot be completely localized on subsets satisfying a condition of negative topological pressure. As an application, one can deduce the existence of a ''strip'' of logarithmic size without eigenvalues below the real axis under this dynamical assumption on the set of undamped trajectories.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Commentaire :

28 pages; compared with version 1, minor modifications, add two references

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL