A shrinking-target problem in the space of unimodular lattices in the three dimensional Euclidean space

2022/10/22 by Reynold Fregoli, Cheng Zheng, Fregoli, Reynold +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 37A17 #Secondary: 11J83 #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2210.12508

openalex publication_date 2022/10/22 · openalex created_date 2022/10/31 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the shrinking-target problem with target at infinity induced by the injectivity radius function under the action of a regular diagonalizable flow on SL₃(\mathbb R)/SL₃(\mathbb Z). In particular, we establish an explicit formula for the Hausdorff dimension of the subset of points p whose orbit approaches the cusp infinitely often with a rate γ≥0.

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