Anisotropic hölder and sobolev spaces for hyperbolic diffeomorphisms

Viviane Baladi, Masato Tsujii

Research output: Contribution to journalArticle

80 Citations (Scopus)

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 Cp functions Cp (V) and of the generalized Sobolev spaces Wp,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.

Original languageEnglish
Pages (from-to)127-154
Number of pages28
JournalAnnales de l'Institut Fourier
Volume57
Issue number1
DOIs
Publication statusPublished - Jan 1 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

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