Sune F Nielsen et al 1999 J. Phys. A: Math. Gen. 32 6757 doi:10.1088/0305-4470/32/39/304
Periodic orbit sum rules for billiards: accelerating cycle expansions
Sune F Nielsen
, Per Dahlqvist and Predrag Cvitanovic
We show that the periodic orbit sums for two-dimensional billiards satisfy an infinity of exact sum rules. We demonstrate their utility by using the flow conservation sum rule to accelerate the convergence of cycle expansions for the overlapping three-disc billiard. The effectiveness of the approach is studied by applying the method on averages, known explicitly by other sum rules. The method is then applied to the Lyapunov exponent.
- PACS
- MSC
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37L30 Attractors and their dimensions, Lyapunov exponents
37C27 Periodic orbits of vector fields and flows
37G15 Bifurcations of limit cycles and periodic orbits
37D50 Hyperbolic systems with singularities (billiards, etc.)
- Subjects
- Dates
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Issue 39 (1 October 1999)
Received 21 December 1998, in final form 2 July 1999
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Periodic orbit sum rules for billiards: accelerating cycle expansions
Sune F Nielsen et al 1999 J. Phys. A: Math. Gen. 32 6757
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