Periodic trajectories of ellipsoidal billiards in the 3-dimensional Minkowski space

TL;DR

This paper analyzes the periodic trajectories of billiards inside ellipsoids in 3D Minkowski space, deriving conditions for periodicity through algebraic, analytic, and polynomial methods.

Contribution

It provides a comprehensive description and new conditions for periodic billiard trajectories in 3D Minkowski space ellipsoids, considering all caustic possibilities.

Findings

Derived conditions for periodicity in algebraic, analytic, and polynomial forms.

Classified all possible caustic configurations for periodic trajectories.

Extended billiard dynamics analysis to Minkowski space geometry.

Abstract

In this paper, we give detailed analysis and description of periodic trajectories of the billiard system within an ellipsoid in the 3-dimensional Minkowski space, taking into account all possibilities for the caustics. The conditions for periodicity are derived in algebro-geometric, analytic, and polynomial form.