Secondary invariants and the singularity of the Ruelle zeta-function in the central critical point

Juhl, Andreas

doi:10.1090/S0273-0979-1995-00570-7

Secondary invariants and the singularity of the Ruelle zeta-function in the central critical point
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Bull. Amer. Math. Soc. 32 (1995), 80-87 Request permission

Abstract:

The Ruelle zeta-function of the geodesic flow on the sphere bundle $S(X)$ of an even-dimensional compact locally symmetric space X of rank 1 is a meromorphic function in the complex plane that satisfies a functional equation relating its values in s and -s. The multiplicity of its singularity in the central critical point s = 0 only depends on the hyperbolic structure of the flow and can be calculated by integrating a secondary characteristic class canonically associated to the flow-invariant foliations of $S(X)$ for which a representing differential form is given.

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