Two applications of Jacobi fields to the billiard ball problem

We present new proofs of two results on the billiard ball problem by Rychlik [R] and Bialy [B]. IntroductionWe will give new proofs of two results on the billiard ball problem by Rychlik [7] and Bialy [1], The original proofs were based on variational considerations.In our approach the variational context is absent, the dynamical system takes the center stage.We hope the simplifications provided by our method will make possible some progress on the conjectures for which these results lend partial support.