Generalized Fredholm determinants and Selberg zeta functions for Axiom A dynamical systems

DOI10.1017/S0143385700009111zbMath0948.37003OpenAlexW2020308435WikidataQ114012334 ScholiaQ114012334MaRDI QIDQ4892471

Hans Henrik Rugh

Publication date: 28 August 2000

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700009111

zbMATH Keywords

Markov partitionsAxiom A flowsgeneralized Selberg zeta functiongeneralized Fredholm determinant

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

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Cites Work

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• An analogue of the prime number theorem for closed orbits of Axiom A flows
• An extension of the theory of Fredholm determinants
• The thermodynamic formalism for expanding maps
• Zeta-functions for expanding maps and Anosov flows
• Resonances in chaotic dynamics
• Meromorphic zeta functions for analytic flows
• The correlation spectrum for hyperbolic analytic maps
• Symbolic Dynamics for Hyperbolic Flows
• Differentiable dynamical systems
• Markov Partitions for Axiom A Diffeomorphisms
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms