Year: 2007
Type: article
Abstract: 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 we give bounds on the essential spectral radii of such extensions in terms of hyperbolicity exponents.
Source: Annales de l’institut Fourier
DOI: 10.5802/aif.2253
Authors: Viviane Baladi, Masato Tsujii
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1843185825