Unexpected Linearly Stable Orbits in $3$-Dimensional Billiards

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...

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Bibliographic Details
Main Author: Attarchi, Hassan
Format: Journal Article
Language:English
Published: 15-11-2021
Subjects:
Mathematics - Dynamical Systems
Online Access:Get full text
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Summary: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.
DOI:10.48550/arxiv.2111.07980