doi:10.3934/dcdss.2009.2.337          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

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