Combinatorial growth in the modular group
Ara Basmajian
CUNY, New York, USARobert Suzzi Valli
Manhattan College, Riverdale, NY, USA
Abstract
We consider an exhaustion of the modular orbifold by compact subsurfaces and show that the growth rate, in terms of word length, of the reciprocal geodesics on such subsurfaces (so named low lying reciprocal geodesics) converges to the growth rate of the full set of reciprocal geodesics on the modular orbifold. We derive a similar result for the low lying geodesics and their growth rate convergence to the growth rate of the full set of closed geodesics
Cite this article
Ara Basmajian, Robert Suzzi Valli, Combinatorial growth in the modular group. Groups Geom. Dyn. 16 (2022), no. 2, pp. 683–703
DOI 10.4171/GGD/667