In integrable Kepler/Hooke billiards with focus/center-aligned conic boundaries, reflected orbit foci lie on a circle or Cassini oval respectively.
A Paris, de l’Imprimerie royale
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Geometric properties of integrable Kepler and Hooke billiards with conic section boundaries
In integrable Kepler/Hooke billiards with focus/center-aligned conic boundaries, reflected orbit foci lie on a circle or Cassini oval respectively.