Ultrametric logarithm laws I

Pages: 337 - 348, Volume 2, Issue 2, June 2009

doi:10.3934/dcdss.2009.2.337       Abstract        Full Text (206.0K)

J. S. Athreya - Department of Mathematics, Princeton University, Fine Hall, Washington Road Princeton NJ 08544-1000, United States (email)
Anish Ghosh - Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200 Austin, Texas 78712, United States (email)
Amritanshu Prasad - The Institute of Mathematical Sciences, CIT campus, Taramani, Chennai 600 113, India (email)

Abstract: We announce ultrametric analogues of the results of Kleinbock-Margulis for shrinking target properties of semisimple group actions on symmetric spaces. The main applications are $S$-arithmetic Diophantine approximation results and logarithm laws for buildings, generalizing the work of Hersonsky-Paulin on trees.

Keywords:  Shrinking target properties, logarithm laws, Diophantine approximation, local fields.
Mathematics Subject Classification:  37A17, 37D40, 11K60.

Received: May 2008;      Revised: November 2008;      Published: April 2009.