Periodic Orbits in Outer Billiard
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چکیده
It is shown that the set of 4-period orbits in outer billiard with piecewise smooth convex boundary has an empty interior, provided the boundary is not a parallelogram.
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Research projects
1 Billiards and related systems 1.1 Polygonal outer billiards in the hyperbolic plane The outer billiard about a convex polygon P in the plane R 2 is a piece-wise isometry, T , of the exterior of P defined as follows: given a point x outside of P , find the support line to P through x having P on the left, and define T (x) to be the reflection of x in the support vertex. See [10, 35]. Figure 1:...
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تاریخ انتشار 2006