Metadata
Abstract
On a closed manifold , we consider a smooth vector field that generates an Anosov flow. Let be a smooth function called potential. It is known that for any , there exists some anisotropic Sobolev space such that the operator has intrinsic discrete spectrum on called Ruelle resonances. In this paper, we show a “Fractal Weyl law”: the density of resonances is bounded by where , and is the Hölder exponent of the distribution (strong stable and unstable). We also obtain some more precise results concerning the wave front set of the resonances and the invertibility of the transfer operator. Since the dynamical distributions are non smooth, we use some semi-classical analysis based on wave packet transform associated to an adapted metric on and construct some specific anisotropic Sobolev spaces.
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