Ruelle zeta function at zero for surfaces

Abstract

We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler characteristic. This result was previously known only in constant curvature.

17 pages. Added Remark 2 on page 1 and revised following the referee's suggestions. To appear in Inventiones Mathematicae

References in corpus (2)

• Power spectrum of the geodesic flow on hyperbolic manifolds
• Anisotropic Sobolev spaces and dynamical transfer operators: C^infty foliations

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