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Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms

Viviane BaladiMasato Tsujii — 2007

Annales de l’institut Fourier

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 p functions C p ( V ) and of the generalized Sobolev spaces W p , t ( V ) , respectively. We then show that the transfer operators associated to  T and a smooth weight g extend boundedly to these spaces, and...

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