A Note On Counting Cuspidal Excursions

B O Stratmann

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For geometrically finite Kleinian groups with parabolic elements we study that part of the Lagrange spectrum which does not lie in the Markov spectrum. Using the ergodicity of the associated geodesic flow with respect to the Liouville Patterson measure, we obtain an estimate for the asymptotic frequency with which recurrent geodesics enter certain cusp regions. In particular, this allows a quantitative description of the logarithmic affinity of geodesic excursions for the cusps.