Abstract
Given a strictly convex plane curve, the dual billiard transformation is the transformation of its exterior defined as follows: given a pointx outside the curve, draw a support line to it from the point and reflectx at the support point. We show that the dual billiard transformation far from the curve is well approximated by the time 1 transformation of a Hamiltonian flow associated with the curve.
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Tabachnikov, S. Asymptotic dynamics of the dual billiard transformation. J Stat Phys 83, 27–37 (1996). https://doi.org/10.1007/BF02183638
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DOI: https://doi.org/10.1007/BF02183638