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Three-Period Orbits in Billiards on the Surfaces of Constant Curvature

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 Added by Vadim Zharnitsky
 Publication date 2011
  fields
and research's language is English




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An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is found that the set of 3-period orbits in billiards on hyperbolic plane, as in the planar case, has zero measure. For the sphere, a new proof of Baryshnikovs theorem is obtained which states that 3-period orbits can form a set of positive measure provided a natural condition on the orbit length is satisfied.



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