Hyperbolic dynamics meet Fourier analysis, an Invitation to the book. Book review of: V. Baladi, Dynamical zeta functions and dynamical determinants for hyperbolic maps. A functional approach

DOI10.1365/s13291-019-00209-6zbMath1451.00044OpenAlexW2974140646MaRDI QIDQ2216531

Frédéric Naud

Publication date: 16 December 2020

Published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1365/s13291-019-00209-6

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02) External book reviews (00A17) Relations between ergodic theory and harmonic analysis (37A46)

Cites Work

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• The thermodynamic formalism for expanding maps
• Meromorphic zeta functions for analytic flows
• Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms
• Banach spaces adapted to Anosov systems
• The correlation spectrum for hyperbolic analytic maps
• Fredholm determinants for hyperbolic diffeomorphisms of finite smoothness
• Ruelle Perron Frobenius spectrum for Anosov maps
• Thermodynamic Formalism
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• The radius of the essential spectrum