Caustics of Poncelet Polygons and Classical Extremal Polynomials

@article{Dragovi2018CausticsOP,
  title={Caustics of Poncelet Polygons and Classical Extremal Polynomials},
  author={Vladimir Dragovi{\'c} and Milena Radnovi{\'c}},
  journal={Regular and Chaotic Dynamics},
  year={2018},
  volume={24},
  pages={1-35}
}
A comprehensive analysis of periodic trajectories of billiards within ellipses in the Euclidean plane is presented. The novelty of the approach is based on a relationship recently established by the authors between periodic billiard trajectories and extremal polynomials on the systems of d intervals on the real line and ellipsoidal billiards in d-dimensional space. Even in the planar case systematically studied in the present paper, it leads to new results in characterizing n periodic… 

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The billiard theory in an active and exciting domain which is closely related to a variety of mathematical fields, like dynamical systems, geometry, group theory, complex analysis, and so on, and so

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