Secondary invariants and the singularity of the Ruelle zeta-function in
the central critical point
by Andreas Juhl
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.
Article Information:
Bulletin Volume 32 Issue 1, January 1995, pages 080-087
Article Type: Research Announcement
MSC: Primary 58F17, 58F20, 11F72; Secondary 58F18, 58F06
TeX Type: amslatex
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