Combinatorial growth in the modular group

Groups, geometry, and dynamics

article

Ara Basmajian¹  Robert Suzzi Valli² 

[1] CUNY;Manhattan College

关键词: Asymptotic growth;    binary words;    closed geodesics;    modular orbifold;   

DOI  :  10.4171/ggd/667

学科分类：神经科学

来源: European Mathematical Society

【 摘 要 】

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.

【 授权许可】

CC BY