Incomplete integrable Hamiltonian systems with complex polynomial Hamiltonian of small degree
- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
Complex Hamiltonian systems with one degree of freedom on C{sup 2} with the standard symplectic structure {omega}C=dz and dw and a polynomial Hamiltonian function f=z{sup 2}+P{sub n}(w), n=1,2,3,4, are studied. Two Hamiltonian systems (M{sub i}, Re{omega}{sub C,i}, H{sub i}=Ref{sub i}), i=1,2, are said to be Hamiltonian equivalent if there exists a complex symplectomorphism M{sub 1}{yields}M{sub 2} taking the vector field sgradH{sub 1} to sgradH{sub 2}. Hamiltonian equivalence classes of systems are described in the case n=1,2,3,4, a completed system is defined for n=3,4, and it is proved that it is Liouville integrable as a real Hamiltonian system. By restricting the real action-angle coordinates defined for the completed system in a neighbourhood of any nonsingular leaf, real canonical coordinates are obtained for the original system. Bibliography: 9 titles.
- OSTI ID:
- 21570925
- Journal Information:
- Sbornik. Mathematics, Vol. 201, Issue 10; Other Information: DOI: 10.1070/SM2010v201n10ABEH004120; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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