165 research outputs found
On the Drach superintegrable systems
Cubic invariants for two-dimensional degenerate Hamiltonian systems are
considered by using variables of separation of the associated St\"ackel
problems with quadratic integrals of motion. For the superintegrable St\"ackel
systems the cubic invariant is shown to admit new algebro-geometric
representation that is far more elementary than the all the known
representations in physical variables. A complete list of all known systems on
the plane which admit a cubic invariant is discussed.Comment: 16 pages, Latex2e+Amssym
Towards a classification of natural bi-hamiltonian systems
For construction and classification of the natural integrable systems we
propose to use a criterion of separability in Darboux--Nijenhuis coordinates,
which can be tested without an a priori explicit knowledge of these
coordinates.Comment: LaTeX 22 page
- …