Equidistribution of divergent geodesics in negative curvature

The paper proves equidistribution and counting for divergent geodesics by (i) reducing divergent geodesics to the compact cores given by common perpendiculars between Margulis cusp neighborhoods, (ii) applying equidistribution of Lebesgue measures along those perpendiculars toward the Bowen–Margulis measure with the normalization δΓ||mBM||/(T e^{δΓ T}), and (iii) lifting this to full geodesic orbits with a uniform O(1/T) trimming error for test functions supported in the thick part. This matches the candidate’s solution step-for-step. Key ingredients in the paper include the bijection and complexity/length identity τ(ℓ)=λ(αℓ) (Lemma 4.1) and counting asymptotics via skinning measures, giving Card ≤T ~ ||σ_T||/(δΓ||mBM||) e^{δΓ T} (Equation (13)), together with δΓ=h_M (Equation (4)). The normalization in the main equidistribution limit is indeed with T·e^{-h_M T}, as is clear from Theorem 5.1 and the derivation culminating in Equation (16); the candidate’s normalization remark is therefore correct. An apparent sign in the displayed formulation of Theorem 1.1 in the snippet looks positive, but the body of the paper consistently uses the negative sign in the exponent and the denominator T e^{δΓ T}, yielding finite limits (Theorem 5.1; Equations (15),(16)) .