Upper bound on the density of Ruelle resonances for Anosov flows

Physics – Mathematical Physics

Scientific paper

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57 pages

Scientific paper

Using a semiclassical approach we show that the spectrum of a smooth Anosov
vector field V on a compact manifold is discrete (in suitable anisotropic
Sobolev spaces) and then we provide an upper bound for the density of
eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real
axis and for large real parts.

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