Obstacles with non-trivial trapping sets in higher dimensions. (English) Zbl 1360.37074
Summary: Using a well-known example of Livshits, for every \({n > 2}\) we construct obstacles \(K\) in \({\mathbb{R}^n}\) such that the set of trapped points for the billiard flow in the exterior of \(K\) has a non-empty interior, and therefore a positive Lebesgue measure.
MSC:
| 37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
| 37D40 | Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
| 53D25 | Geodesic flows in symplectic geometry and contact geometry |
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
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