The convergence of zeta functions for certain geodesic flows depends on their pressure

DOI10.1007/BF01214614zbMath0437.58016MaRDI QIDQ1141405

Anthony Manning, Su-Shing Chen

Publication date: 1981

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/183651

zbMATH Keywords

pressureRiemannian manifoldzeta functionnegative curvatureSelberg trace formula suggests

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Geodesic flows in symplectic geometry and contact geometry (53D25) Ergodic theory (37A99) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (6)

Zeta functions and periodic orbit theory: A review ⋮ The pressure of the geodesic flow on a negatively curved manifold ⋮ Entropy of geodesic flow and exponent of convergence of some Dirichlet series ⋮ On the spectral theory and dynamics of asymptotically hyperbolic manifolds ⋮ Repellers for real analytic maps ⋮ An analogue of the prime number theorem for closed orbits of shifts of finite type and their suspensions

Cites Work

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• Topological entropy for geodesic flows
• The ergodic theory of axiom A flows
• Zeta-functions for expanding maps and Anosov flows
• Closed geodesics and the \(\eta\)-invariant
• Some systems with unique equilibrium states
• A Variational Principle for the Pressure of Continuous Transformations
• Length spectrum for compact locally symmetric spaces of strictly negative curvature
• Flows with Unique Equilibrium States
• Differentiable dynamical systems
• GIBBS MEASURES IN ERGODIC THEORY

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