Periodic Billiards Within Conics in the Minkowski Plane and Akhiezer Polynomials

@article{Adabrah2019PeriodicBW,
  title={Periodic Billiards Within Conics in the Minkowski Plane and Akhiezer Polynomials},
  author={Anani Komla Adabrah and Vladimir Dragovi{\'c} and Milena Radnovi{\'c}},
  journal={Regular and Chaotic Dynamics},
  year={2019},
  volume={24},
  pages={464 - 501}
}
We derive necessary and sufficient conditions for periodic and for elliptic periodic trajectories of billiards within an ellipse in the Minkowski plane in terms of an underlining elliptic curve. We provide several examples of periodic and elliptic periodic trajectories with small periods. We observe a relationship between Cayley-type conditions and discriminantly separable and factorizable polynomials. Equivalent conditions for periodicity and elliptic periodicity are derived in terms of… 
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