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A UNIFORM DISTRIBUTION RESULT FOR A BILLIARD IN A UNIT SQUARE

Published online by Cambridge University Press:  29 November 2005

E. ALKAN ,
T. V. SELVAKUMARAN  and
A. ZAHARESCU
E. ALKAN
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL, 61801, USA e-mail: alkan@math.uiuc.edu, selvkmrn@math.uiuc.edu, zaharesc@math.uiuc.edu
T. V. SELVAKUMARAN
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL, 61801, USA e-mail: alkan@math.uiuc.edu, selvkmrn@math.uiuc.edu, zaharesc@math.uiuc.edu
A. ZAHARESCU
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL, 61801, USA e-mail: alkan@math.uiuc.edu, selvkmrn@math.uiuc.edu, zaharesc@math.uiuc.edu
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Abstract

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In this paper we establish a uniform distribution result for the time spent by a billiard particle in the unit square having vertices (0,0), (1,0), (1,1), (0,1), with small triangular pockets of size $\epsilon$ removed from its corners.

Keywords

11B5711K36
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 3 , September 2005 , pp. 529 - 547
Copyright
2005 Glasgow Mathematical Journal Trust