Ultrametric logarithm laws I

J. S. Athreya; Anish Ghosh; Amritanshu Prasad

doi:10.3934/dcdss.2009.2.337

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2009, Volume 2, Issue 2: 337-348. Doi: 10.3934/dcdss.2009.2.337

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Ultrametric logarithm laws I

1.
Department of Mathematics, Princeton University, Fine Hall, Washington Road Princeton NJ 08544-1000
2.
Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200 Austin, Texas 78712
3.
The Institute of Mathematical Sciences, CIT campus, Taramani, Chennai 600 113

Received: April 30, 2008

Revised: October 31, 2008

Published: May 2009

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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.

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Mathematics Subject Classification: 37A17, 37D40, 11K60.

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