Functiones et Approximatio Commentarii Mathematici

A parity problem on the free path length of a billiard in the unit square with pockets

Andrew H. Ledoan, Alexandru Zaharescu, and Emre Alkan

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Abstract

We present a result on short intervals about the moments of the free path length of the linear trajectory of a billiard in the unit square with small triangular pockets of size $\varepsilon$ removed at the corners, in which the trajectory ends in a specified corner pocket.

Article information

Source
Funct. Approx. Comment. Math. Volume 35, Number 1 (2006), 19-36.

Dates
First available in Project Euclid: 16 December 2008

Permanent link to this document
http://projecteuclid.org/euclid.facm/1229442614

Mathematical Reviews number (MathSciNet)
MR2271604

Zentralblatt MATH identifier
1128.11042

Digital Object Identifier
doi:10.7169/facm/1229442614

Subjects
Primary: 37D50: Hyperbolic systems with singularities (billiards, etc.)
Secondary: 11B57: Farey sequences; the sequences ${1^k, 2^k, \cdots}$ 11P21: Lattice points in specified regions 82C40: Kinetic theory of gases

Keywords
Billiards periodic Lorentz gas free path length Farey fractions visible points Kloosterman sums

Citation

Alkan, Emre; Ledoan, Andrew H.; Zaharescu, Alexandru. A parity problem on the free path length of a billiard in the unit square with pockets. Funct. Approx. Comment. Math. 35 (2006), no. 1, 19--36. doi:10.7169/facm/1229442614. http://projecteuclid.org/euclid.facm/1229442614.


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