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Some spectral results for damped wave equations on Zoll manifoldsMathematical Physics & Probability
|Speaker: ||Dr. Michael Hitrik, UC Berkeley|
|Location: ||693 Kerr|
|Start time: ||Tue, Nov 7 2000, 3:10PM|
The eigenfrequencies associated to a damped wave equation on a compact
Riemannian manifold are known to belong to a band parallel to the real axis.
Under the assumption of periodicity of the geodesic flow we study the asymptotic
distribution of the eigenfrequencies inside the band. We show that the
eigenfrequencies form clusters determined by the Morse index of the closed
geodesics and the damping coefficient averaged along the geodesic flow. The
asymptotics for the multiplicities of the clusters are obtained.