## Billiards that share a triangular caustic |

E.Gutkin and |
O. Knill |

This proceedings paper has appeared in the volume " New trends in Hamiltonian systms and Celestial Mechanics ", " Second International symposium on Hamiltonian Systems and Celestial Mechanics ", Advanced Series in Nonlinear Dynamics, Vol. 8 World Scientific, Singapore, 1996. |

## Abstract |
We consider a one-parameter family of billiard tables which have as a common caustic the equilateral triangle . The billiard tables are constructed geometrically by the string construction, where the length of the string is the parameter. We study the family of circle homeomorphisms obtained by restricting the billiard map to the canonical invariant circle belonging to the caustic and the rotation function . We show that the graph of is a devil's staircase. We analyze the passage of a Birkhoff periodic orbits through the caustic as the parameter changes. |
---|