Prime orbit theorems with multi-dimensional constraints for Axiom A flows

DOI10.1007/BF01299384zbMath0765.58025OpenAlexW2057976497WikidataQ114693970 ScholiaQ114693970MaRDI QIDQ1207646

Richard Sharp

Publication date: 12 May 1993

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178591

zbMATH Keywords

\(L\)-functionshomologyAnosov flowsclosed orbitsAxiom A flow

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems with hyperbolic behavior (37D99)

Related Items (13)

Orbit counting for some discrete groups acting on simply connected manifolds with negative curvature ⋮ Helicity, linking and the distribution of null-homologous periodic orbits for Anosov flows* ⋮ Large deviation asymptotics for Anosov flows ⋮ Global normal form and asymptotic spectral gap for open partially expanding maps ⋮ Closed orbits in quotient systems ⋮ Correlation of the renormalized Hilbert length for convex projective surfaces ⋮ Counting Closed Orbits in Discrete Dynamical Systems ⋮ Closed geodesics and periods of automorphic forms ⋮ Precise counting results for closed orbits of Anosov flows ⋮ The correlation of length spectra of two hyperbolic surfaces ⋮ Multifractal analysis of Birkhoff averages for some self-affine IFS ⋮ A central limit theorem for periodic orbits of hyperbolic flows ⋮ Higher Teichmüller Theory for Surface Groups and Shifts of Finite Type

Cites Work

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• An analogue of the prime number theorem for closed orbits of Axiom A flows
• Closed orbits in homology classes
• Closed geodesics in homology classes on surfaces of variable negative curvature
• Distribution of periodic orbits of symbolic and axiom A flows
• Some inverse spectral results for negatively curved 2-manifolds
• The central limit theorem for geodesic flows on \(n\)-dimensional manifolds of negative curvature
• Asymptotic cycles
• Expansive one-parameter flows
• The Chebotarov theorem for Galois coverings of Axiom A flows
• Homology and Closed Geodesics in a Compact Negatively Curved Surface
• Bowen's equidistribution theory and the Dirichlet density theorem
• A complex Ruelle-Perron-Frobenius theorem and two counterexamples
• Symbolic Dynamics for Hyperbolic Flows
• On the entropy of a flow
• Axiom A Diffeomorphisms have Rational Zeta Functions
• GIBBS MEASURES IN ERGODIC THEORY
• The Equidistribution of Closed Geodesics
• Periodic Orbits for Hyperbolic Flows
• Généralisation du théorème de Ikehara
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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