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.
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