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arXiv · 2111.07980

Unexpected Linearly Stable Orbits in $3$-Dimensional Billiards

Hassan Attarchi
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Abstract

In this work, we construct linearly stable periodic orbits in $3$-dimensional domains with boundaries containing focusing components (small pieces of a sphere) where we place these components arbitrarily far apart. It demonstrates that we cannot directly implement the construction methods of planar billiards with focusing boundaries and chaotic properties into $3$-dimensional billiards.

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Hassan Attarchi. 2021-11-15. Unexpected Linearly Stable Orbits in $3$-Dimensional Billiards. https://doi.org/10.1016/j.physd.2022.133260

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