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

• Reynold Fregoli ^[1] ; Cheng Zheng ^[2]
  1. [1] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     
  2. [2] School of Mathematical Sciences, China
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 3, 2024, págs. 1-62
• Idioma: inglés
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• Resumen

  • 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(R)/ SL3(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.