Delocalization of slowly damped eigenmodes ...
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
Delocalization of slowly damped eigenmodes on Anosov manifolds
Author(s) :
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
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]
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 >
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
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