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Local instability of orbits in polygonal and polyhedral billiards. (English) Zbl 0924.58043
Summary: We classify when local instability of orbits of closely points can occur for billiards in two-dimensional polygons, for billiards inside three-dimensional polyhedra and for geodesic flows on surfaces of three-dimensional polyhedra. We sharpen a theorem of Boldrighini, Keane and Marchetti. We show that polygonal and polyhedral billiards have zero topological entropy. We also prove that billiards in polygons are positive expansive when restricted to the set of non-periodic points. The methods used are elementary geometry and symbolic dynamics.

37A99 Ergodic theory
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
Full Text: DOI
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