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- W2123123462 abstract "We prove a Weyl-type fractal upper bound for the spectrum of the damped wave equation, on a negatively curved compact manifold. It is known that most of the eigenvalues have an imaginary part close to the average of the damping function. We count the number of eigenvalues in a given horizontal strip deviating from this typical behaviour; the exponent that appears naturally is the “entropy” that gives the deviation rate from the Birkhoff ergodic theorem for the geodesic flow. A Weyl-type lower bound is still far from reach; but in the particular case of arithmetic surfaces, and for a strong enough damping, we can use the trace formula to prove a result going in this direction." @default.
- W2123123462 created "2016-06-24" @default.
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- W2123123462 date "2010-07-16" @default.
- W2123123462 modified "2023-10-14" @default.
- W2123123462 title "Spectral Deviations for the Damped Wave Equation" @default.
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- W2123123462 doi "https://doi.org/10.1007/s00039-010-0071-x" @default.
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