Abstract
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.
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Noakes, L., Stoyanov, L. Obstacles with non-trivial trapping sets in higher dimensions. Arch. Math. 107, 73–80 (2016). https://doi.org/10.1007/s00013-016-0907-1
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DOI: https://doi.org/10.1007/s00013-016-0907-1