Anisotropic hölder and sobolev spaces for hyperbolic diffeomorphisms

Viviane Baladi, Masato Tsujii

研究成果: Contribution to journalArticle査読

87 被引用数 (Scopus)

抄録

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.

本文言語英語
ページ(範囲)127-154
ページ数28
ジャーナルAnnales de l'Institut Fourier
57
1
DOI
出版ステータス出版済み - 2007
外部発表はい

All Science Journal Classification (ASJC) codes

  • 代数と数論
  • 幾何学とトポロジー

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