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The differential zeta function for axiom A attractors. (English) Zbl 0702.58040

The main result of the paper is the following Theorem. Let \(\phi_ t: \Lambda \to \Lambda\) be a \(C^{\infty}\) Axiom A flow restricted to an attractor \(\Lambda\), for which the unstable bundle is one-dimensional, then the differential zeta function \(\zeta^{\mu}(s)\) has a meromorphic extension to the entire complex plane \({\mathbb{C}}.\)
As an application, some consequences on geodesic flows for compact surfaces of (variable) negative curvature are derived.
Reviewer: J.Szilasi

MSC:

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
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