 02250 Fernando Cardoso, Georgi Popov
 Quasimodes with Exponentially Small Errors
Associated with Elliptic Periodic Rays
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Jun 2, 02

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Abstract. The aim of this paper is to construct compactly supported
Gevrey quasimodes with exponentially
small discrepancy for the Laplace
operator with Dirichlet boundary conditions in a domain $X$ with
analytic boundary.
The quasimodes are associated with a nondegenerate elliptic closed
broken geodesic $\gamma$ in $X$. We find a Cantor family $\Lambda$ of
invariant tori of the corresponding Poincar map which is Gevrey
smooth with respect to the transversal variables (the frequencies).
Quantizing the Gevrey family $\Lambda$, we construct quasimodes with
exponentially small discrepancy. As a consequence, we
obtain a large amount of resonances
exponentially close to the real axis for suitable compact obstacles.
This is a new version of mparc 02181, where the beginning of
the proof of Proposition 6.1 is revised.
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