Abstract
We study complex Hamiltonian systems on ℂ × (ℂ \ {0}) with the standard symplectic structure ωℂ = dz^dw and Hamiltonian function f = az 2+b/w+P n (w), where P n (w) is a polynomial of degree n, the numbers a, b ∈ ℂ, and ab ≠ 0. For some natural classes of these ℂ-Hamiltonian systems, an equivalence relation in the Hamiltonian sense is studies and the topology of the corresponding quotient space is determined. It is also proved that for ℂ-Hamiltonian systems with the Hamiltonian function f = az 2 + b/w + P n (w), where ab ≠ 0, n ≥ 0, the bifurcation complex is homeomorphic to a two-dimensional plane.
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Original Russian Text © N.N. Martynchuk. 2015, published in Vestnik Moskovskogo Universiteta, Maternatika. Mekhanika, 2015, Vol. 70, No. 2, pp. 3–9.
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Martynchuk, N.N. Complex Hamiltonian systems on ℂ2 with Hamiltonian function of low laurent degree. Moscow Univ. Math. Bull. 70, 53–59 (2015). https://doi.org/10.3103/S0027132215020011
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DOI: https://doi.org/10.3103/S0027132215020011