2013/03/24 by Lei Yang, Yang, Lei
Mathematics · #22E40 #37A17 #37A25 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1303.5993
openalex publication_date 2013/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we consider the product space of several non-compact finite volume hyperbolic spaces, V1, V2, … , Vk of dimension n. Let T1(Vi) denote the unit tangent bundle of Vi for each i=1,… , k, then for every (v1, … , vk) ∈ T1 (V1) × ⋯ × T1 (Vk), the diagonal geodesic flow gt is defined by gt (v1, … , vk) = (gt v1, … , gt vk). And we define \mathfrakDk =\ (v1, …, vk) ∈ T1 (V1) × ⋯ × T1 (Vk): gt(v1, …, vk) divergent, as t→ ∞\. We will prove that the Hausdorff dimension of \mathfrakDk is equal to k(2n-1) - (n-1)/(2). This extends the result of Yitwah Cheung ~\citeCheung1.