### 8.3 Geodesic loop

Consider a solution with asymptotics of the form of Equations (37) – (38) and . Then
converges and tends to infinity as . In other words, for a fixed , the solution
roughly speaking goes to the boundary along a geodesic in hyperbolic space; see Equation (21). Since
and , for a fixed , define a loop in hyperbolic space, the solution is asymptotically approximated by a
“loop of geodesics”.