Circum- and Inconic Invariants of 3-Periodics in the Elliptic Billiard
arXiv:2004.02680v42 citations
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This work addresses geometric invariants in dynamical systems, specifically for researchers in billiard dynamics and conic geometry, and appears incremental as it builds on known families of periodic orbits.
The paper investigates the geometry of circumconics and inconics associated with 3-periodic orbits in an elliptic billiard, identifying invariants like aspect ratio and pairwise focal length ratios.
A Circumconic passes through a triangle's vertices; an Inconic is tangent to the sidelines. We study the variable geometry of certain conics derived from the 1d family of 3-periodics in the Elliptic Billiard. Some display intriguing invariances such as aspect ratio and pairwise ratio of focal lengths.