Periodic billiard orbits on $n$--dimensional ellipsoids with impacts on confocal quadrics and isoperiodic deformations

TL;DR

This paper investigates the behavior of periodic geodesic trajectories on multi-dimensional ellipsoids with impacts on confocal quadrics, demonstrating the applicability of isoperiodic deformation methods to analyze these systems.

Contribution

It introduces the use of isoperiodic deformation techniques to study periodic billiard orbits on n-dimensional ellipsoids with impacts on confocal quadrics, extending previous approaches.

Findings

Isoperiodic deformation applies to multidimensional billiard systems.

Periodic geodesic motion can be characterized on ellipsoids with impacts.

Method provides new insights into the structure of periodic orbits.

Abstract

In our paper we study periodic geodesic motion on multidimensional ellipsoids with elastic impacts along confocal quadrics. We show that the method of isoperiodic deformation is applicable.