The topology of Lagrangian foliations of integrable systems with hyperelliptic Hamiltonian
- M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
We study the integrable Hamiltonian systems (C{sup 2},Re(dz and dw),H=Ref(z,w)) with the additional first integral F=Imf which correspond to the complex Hamiltonian systems (C{sup 2},dz and dw,f(z,w)) with a hyperelliptic Hamiltonian f(z,w)=z{sup 2}+P{sub n}(w), n element of N. For n{>=}3 the system has incomplete flows on any Lagrangian leaf f{sup -1}(a). The topology of the Lagrangian foliation of such systems in a small neighbourhood of any leaf f{sup -1}(a) is described in terms of the number n and the combinatorial type of the leaf--the set of multiplicities of the critical points of the function f that belong to the leaf. For odd n, a complex analogue of Liouville's theorem is obtained for those systems corresponding to polynomials P{sub n}(w) with simple real roots. In particular, a set of complex canonical variables analogous to action-angle variables is constructed in a small neighbourhood of the leaf f{sup -1}(0). Bibliography: 12 titles.
- OSTI ID:
- 21592560
- Journal Information:
- Sbornik. Mathematics, Vol. 202, Issue 3; Other Information: DOI: 10.1070/SM2011v202n03ABEH004150; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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