## Ping-pong groups and closed geodesics in constant negative curvature. (Groupes du ping-pong et géodésiques fermées en courbure $$-1$$.)(French)Zbl 0853.53032

Summary: We consider a class of free and discrete groups of isometries of the hyperbolic ball $${\mathbb B}^d$$ which contain parabolic transformations and we prove that the number of closed geodesics on $${\mathbb B}^d/\Gamma$$ whose length is less than $$a$$ is equivalent to $${e^{a\delta}\over a\delta}$$, where $$\delta$$ is the critical exponent of the Poincaré series.

### MSC:

 53C22 Geodesics in global differential geometry
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### References:

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