Unexpected Linearly Stable Orbits in $3$-Dimensional Billiards

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.

10 pages, 3 figures

References in corpus (2)

• Physical Versus Mathematical Billiards: From Regular Dynamics to Chaos and Back
• Collision of a Hard Ball with Singular Points of the Boundary