Exact smooth classification of hamiltonian vector fields on two-dimensional manifolds
A complete exact classification of Hamiltonian systems with Morse Hamiltonians on two-dimensional manifolds is given, i.e., the systems are classified up to diffeomorphisms mapping vector fields into vector fields. The classification imposes no restrictions on Morse functions.
Key wordsHamiltonian vector field two-dimensional manifold germ Morse function letter-atom deformation retract
Unable to display preview. Download preview PDF.
- 1.A. V. Bolsinov and A. T. Fomenko, “Trajectory equivalence of integrable Hamiltonian systems with two degrees of freedom: classification theorem. I”,Mat. Sb. [Russian Acad. Sci. Sb. Math.],185, No. 5, 27–78 (1994).Google Scholar
- 4.L. H. Elliason, “Normal forms for Hamiltonian systems with Poisson commuting integrals. Elliptic case”,Comm. Math. Helv.,65, No. 1, 4–35 (1990).Google Scholar
- 7.A. T. Fomenko,Symplectic Geometry: Methods and Applications [in Russian], Izd. Moskov. Univ., Moscow (1966).Google Scholar