Unbounded Orbits for Semicircular Outer Billiard

Abstract.

We show that the outer billiard around a semicircle has an open ball escaping to infinity.

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Correspondence to Dmitry Dolgopyat.

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Submitted: April 19, 2008.; Accepted: January 11, 2009.

Communicated by Domokos Szasz.

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Dolgopyat, D., Fayad, B. Unbounded Orbits for Semicircular Outer Billiard. Ann. Henri Poincaré 10, 357–375 (2009). https://doi.org/10.1007/s00023-009-0409-9

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Keywords

  • Normal Form
  • Lower Region
  • Region Versus
  • Coordinate Change
  • Piecewise Polynomial