Unexpected linearly stable orbits in 3-dimensional billiards (Q2140103)

The author shows that for 3-dimensional billiards in a sphere there exist special linearly stable periodic orbits associated to some edges of a cube. The analysis makes use of a Jacobi field and its evolution for the billiard orbit. After a short and general introduction the author proves rigorously his results. The abstract provides in a clear and compact way all relevant information contained and worked out in the paper. The references given in the work support and complement the results.