Topological invariants of Liouville integrable Hamiltonian systems
Let Q be a compact three-dimensional isoenergetic surface for a Hamiltonian system and f a second integral on Q. Then it is possible to construct a certain graph \(\Gamma\) (Q,f) (in the sense of graph theory). Using the graph \(\Gamma\) (Q,f), the author presents three topological invariants of Hamiltonian systems that are integrable in the sense of Liouville. The integrable cases are characterized by these invariants independently of the choice of second integral. The invariants permit us to classify the integrable systems up to topological equivalence. In addition, the isoenergetic surfaces of the integrable systems can be classified by these invariants. For some classical integrable systems the invariants are calculated.
topological invariants of Hamiltonian systems
scientific article; zbMATH DE number 4143084
scientific article