Two-link billiard trajectories: Extremal properties and stability (Q2761363)

The author studies two-link periodic trajectories of convex plane billiard. The main result is the following assertion. Let caustic of the convex oval \(\Gamma\) do not intersect \(\Gamma\) and the function \( L\: T\to R \) possess only degenerate stationary points. Then the billiard within \(\Gamma\) has an even number \( m\geq 2 \) of two-link periodic trajectories and moreover, a half of them are hyperbolic while the other half are elliptic. An example of billiard is presented whose caustic intersect s the boundary and all two-link trajectories are hyperbolic.