We give an asymptotic estimate for the number of periodic
orbits of an Anosov flow which are subject to multi-dimensional constraints.
We also study their spatial distribution. For instance, we describe the
distribution of periodic orbits with respect to homology classes, for both
homologically full Anosov flows and suspensions of Anosov transformations.
Abstract. -We consider a large class of non compact hyperbolic manifolds M = H n /Γ with cusps and we prove that the winding process (Yt) generated by a closed 1-form supported on a neighborhood of a cusp C, satisfies a limit theorem, with an asymptotic stable law and a renormalising factor depending only on the rank of the cusp C and the Poincaré exponent δ of Γ. No assumption on the value of δ is required and this theorem generalises previous results due to Y.
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