Anisotropic Hölder and Sobolev Spaces for Hyperbolic Diffeomorphisms
نویسندگان
چکیده
We study spectral properties of transfer operators for diffeomorphisms T : X → X on a Riemannian manifold X: Suppose that Ω is an isolated hyperbolic subset for T , with a compact isolating neighborhood V ⊂ X. We first introduce Banach spaces of distributions supported on V , which are anisotropic versions of the usual space of C functions C(V ) and of the generalized Sobolev spaces W (V ), respectively. Then we show that the transfer operators associated to T and a smooth weight g extend boundedly to these spaces, and we give bounds on the essential spectral radii of such extensions in terms of hyperbolicity exponents.
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