%0 Journal Article %T Upper bound on the density of Ruelle resonances for Anosov flows %A Fr¨¦d¨¦ric Faure %A Johannes Sjoestrand %J Mathematics %D 2010 %I arXiv %R 10.1007/s00220-011-1349-z %X 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. %U http://arxiv.org/abs/1003.0513v1