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Numerical computation of orbits

The following pictures show the reduced phase space of billiard map, where the dihedral symmetry has been factored out. The horizontal tex2html_wrap_inline583 -axes gives the place of impact from 0 to tex2html_wrap_inline587 and the vertical tex2html_wrap_inline589 axes parameterizes the angle of impact. For each of the 14 parameter values we see 13 x 11 orbits each with 100 iterations.

p=1.0
p=1.001 p=1.01 p=1.1
p=1.4 p=1.5 p=1.6
p=1.8 p=1.9 p=1.95
p=2.0
p=2.1 p=3.0 p=4.0

Oliver Knill, Jul 10 1998