Delocalization of slowly damped eigenmodes on Anosov manifolds

Details Delocalization of slowly damped eigenmodes on Anosov manifolds Delocalization of slowly damped eigenmodes on Anosov manifolds

2011-09-09

arxiv.org/abs/1109.1909v2

Physics

Mathematical Physics

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

Scientific paper

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.

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