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

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.

Latex, 28 pages, 3 figures

References in corpus (4)

• Cayley-Type Conditions for Billiards within $k$ Quadrics in $R^d$
• Closed geodesics and billiards on quadrics related to elliptic KdV solutions
• Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation
• Algebraic Closed Geodesics on a Triaxial Ellipsoid

Cited by in corpus (1)

• Periodic ellipsoidal billiard trajectories and extremal polynomials