Billiards in confocal quadrics as a pluri-Lagrangian system
Yuri B. Suris
TL;DR
This paper explores the integrable structure of billiard systems within confocal quadrics using the framework of pluri-Lagrangian systems, highlighting their commuting properties and underlying geometric features.
Contribution
It demonstrates how billiard maps in confocal quadrics form a one-dimensional pluri-Lagrangian system, providing new insights into their integrability and geometric structure.
Findings
Billiard maps in confocal quadrics commute.
The system exhibits a pluri-Lagrangian structure.
Geometric properties underpin integrability.
Abstract
We illustrate the theory of one-dimensional pluri-Lagrangian systems with the example of commuting billiard maps in confocal quadrics.
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