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Two-link billiard trajectories: Extremal properties and stability. (English. Russian original) Zbl 0979.37011
J. Appl. Math. Mech. 64, No. 6, 903-907 (2000); translation from Prikl. Mat. Mekh. 64, No. 6, 942-946 (2000).
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.

MSC:
37C75 Stability theory for smooth dynamical systems
37D05 Dynamical systems with hyperbolic orbits and sets
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
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