Dynamical Zeta Functions in the Nonorientable Case

Abstract

We use a simple argument to extend the microlocal proofs of meromorphicity of dynamical zeta functions to the nonorientable case. In the special case of geodesic flow on a connected non-orientable negatively curved closed surface, we compute the order of vanishing of the zeta function at the zero point to be the first Betti number of the surface.

arXiv comment15 pages

References in corpus (3)

• Pollicott-Ruelle resonances for open systems
• Ruelle zeta function at zero for surfaces
• Dynamical zeta functions for Axiom A flows

Cited by in corpus (3)

• The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds
• Analytic torsion, dynamical zeta function, and the Fried conjecture for admissible twists
• Pollicott-Ruelle resolvent and Sobolev regularity