Title :

Delocalization of slowly damped eigenmodes on Anosov manifolds

Author(s) :

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

Journal title :

Communications in Mathematical Physics

Pages :

555-593

Publisher :

Springer Verlag

Publication date :

2012-11-11

ISSN :

0010-3616

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Comment :

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

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL