Titlebook: Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps; A Functional Approac Viviane Baladi Book 2018 Springer Internation

真

污秽

Manganmics and weights, replacing the Hölder spaces by Sobolev spaces. The chapter ends with the Gouëzel-Keller-Liverani perturbation theory, which will also be applicable in the hyperbolic setting of Part II.

痛打

制造

Chromphism on a hyperbolic basic set and a differentiable weight function. The operator acts on two scales of anisotropic spaces of distributions on the manifold defined using cones (in the cotangent space) adapted to the diffeomorphism.

Triglyceride

Zinneighted dynamical determinant, giving a lower bound on the disc in which this determinant is analytic and where its zeroes admit a spectral interpretation. We apply the results obtained on the weighted dynamical determinant to study the dynamical zeta function.

诙谐

Wolfram SRB measures, in the spirit of the work of Gouëzel-Liverani, recovering classical results of existence, uniqueness, and exponential mixing. Then we present Tsujii’s unpublished proof of Anosov’s theorem using anisotropic spaces.

淘气

https://doi.org/10.1007/978-3-319-77661-3dynamical zeta functions; Ruelle transfer operators; Anosov diffeomorphisms; anisotropic Banach Spaces;

通情达理

除草剂

Smooth expanding maps: The spectrum of the transfer operatormics and weights, replacing the Hölder spaces by Sobolev spaces. The chapter ends with the Gouëzel-Keller-Liverani perturbation theory, which will also be applicable in the hyperbolic setting of Part II.

性别

Smooth expanding maps: Dynamical determinantspanding dynamics and weights. The proof uses the Milnor-Thurston kneading operator approach. The contents of this chapter are a blueprint for the technically more involved situation of hyperbolic dynamics and the corresponding anisotropic Banach spaces in Part II.