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Preprints, Working Papers, ... Year : 2012

Density and localization of resonances for convex co-compact hyperbolic surfaces

Abstract

Let $X$ be a convex co-compact hyperbolic surface and let $\delta$ be the Hausdorff dimension of the limit set of the underlying discrete group. We show that the density of the resonances of the Laplacian in strips $\{ \sigma\leq \re(s) \leq \delta \}$ with $\vert \im(s) \vert \leq T$ is less than $O(T^{1+\delta-\epsilon(\sigma)})$ with $\epsilon>0$ as long as $\sigma>\delta/2$. This improves the fractal Weyl upper bounds of Zworski and supports numerical results obtained for various models of quantum chaotic scattering.
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Dates and versions

hal-00680801 , version 1 (20-03-2012)

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Frédéric Naud. Density and localization of resonances for convex co-compact hyperbolic surfaces. 2012. ⟨hal-00680801⟩

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UNIV-AVIGNON
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