When different norms lead to same billiard trajectories?

@article{Akopyan2019WhenDN,
  title={When different norms lead to same billiard trajectories?},
  author={Arseniy V. Akopyan and Roman N. Karasev},
  journal={arXiv: Metric Geometry},
  year={2019}
}
In this paper, extending the works of Milena Radnovic and Serge Tabachnikov, we establish conditions for two different non-symmetric norms to define the same billiard reflection law. 

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