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Prime orbit theorems with multi-dimensional constraints for Axiom A flows. (English) Zbl 0765.58025
We give a new proof of an asymptotic formula for the number of closed orbits of a weak-mixing Axiom A flow subject to certain constraints due to S. Lalley. We extend this result to cover the case of finite group extensions and, for transitive Anosov flows, give an application to homology. We also discuss asymptotics for closed orbits in a fixed homology class, extending a result of A. Katsuda and T. Sunada.
Reviewer: R.Sharp (Warwick)

##### MSC:
 37D99 Dynamical systems with hyperbolic behavior 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics
##### Keywords:
$$L$$-functions; closed orbits; Axiom A flow; Anosov flows; homology
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##### References:
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