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Let S be the Euclidean plane, the hyperbolic plane or a hemisphere of the unit sphere. The convex billiard problem consist on the free motion of a particle inside a geodesically convex bounded region on S, making elastic collisions at the impacts with the boundary. This problem defines a class of area preserving twist diffeomorphisms, giving rise to 2-dimensional conservative dynamical systems.
In this work we will present the generic dynamics of such billiards, and show they exhibit the richness of the dynamics of conservative systems. |
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