Unexpected Linearly Stable Orbits in $3$-Dimensional Billiards

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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