On curves with the Poritsky property

@article{Glutsyuk2019OnCW,
  title={On curves with the Poritsky property},
  author={A. A. Glutsyuk},
  journal={Journal of Fixed Point Theory and Applications},
  year={2019},
  volume={24},
  pages={1-60}
}
  • A. Glutsyuk
  • Published 7 January 2019
  • Mathematics
  • Journal of Fixed Point Theory and Applications
Reflection in planar billiard acts on oriented lines. For a given closed convex planar curve $$\gamma $$ γ , the string construction yields a one-parameter family $$\Gamma _p$$ Γ p of nested billiard tables containing $$\gamma $$ γ for which $$\gamma $$ γ is a caustic: the reflection from $$\Gamma _p$$ Γ p sends each tangent line to $$\gamma $$ γ to a line tangent to $$\gamma $$ γ . The reflections from $$\Gamma _p$$ Γ p act on the corresponding tangency points, inducing a family of string… 

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