Next: A Family of Billiard


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 tex2html_wrap_inline402 which have as a common caustic the equilateral triangle tex2html_wrap_inline404 . The billiard tables tex2html_wrap_inline402 are constructed geometrically by the string construction, where the length tex2html_wrap_inline408 of the string is the parameter. We study the family of circle homeomorphisms tex2html_wrap_inline410 obtained by restricting the billiard map to the canonical invariant circle tex2html_wrap_inline412 belonging to the caustic and the rotation function tex2html_wrap_inline414 . We show that the graph of tex2html_wrap_inline416 is a devil's staircase. We analyze the passage of a Birkhoff periodic orbits through the caustic as the parameter changes.

Oliver Knill, HTML translation made on July 8, 1998