Vesselin Petkov and Luchezar Stoyanov 2009 Nonlinearity 22 2657 doi:10.1088/0951-7715/22/11/005
Correlations for pairs of periodic trajectories for open billiards
Vesselin Petkov1 and Luchezar Stoyanov2
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In this paper we prove two asymptotic estimates for pairs of closed trajectories for open billiards similar to those established by Pollicott and Sharp (2006 Invent. Math. 163 10–24) for closed geodesics on negatively curved compact surfaces. The first of these estimates holds for general open billiards in any dimension. The more intricate second estimate is established for open billiards satisfying the so-called Dolgopyat type estimates. This class of billiards includes all open billiards in the plane and open billiards in 
(N ≥ 3) satisfying some additional conditions.
- PACS
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05.45.-a Nonlinear dynamics and nonlinear dynamical systems
- MSC
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37D50 Hyperbolic systems with singularities (billiards, etc.)
- Subjects
- Dates
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Issue 11 (November 2009)
Received 11 June 2009, in final form 11 September 2009
Published 5 October 2009
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Correlations for pairs of periodic trajectories for open billiards
Vesselin Petkov and Luchezar Stoyanov 2009 Nonlinearity 22 2657
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