Geodesic
Complex Hamiltonian systems on $\mathbb{C^2}$ with Hamiltonian function of low Laurent degree
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2015), pp. 3-9 
N. N. Martynchuk. Complex Hamiltonian systems on $\mathbb{C^2}$ with Hamiltonian function of low Laurent degree. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2015), pp. 3-9. http://geodesic.mathdoc.fr/item/VMUMM_2015_2_a0/
@article{VMUMM_2015_2_a0,
     author = {N. N. Martynchuk},
     title = {Complex {Hamiltonian} systems on $\mathbb{C^2}$ with {Hamiltonian} function of low {Laurent} degree},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--9},
     year = {2015},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_2_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study complex Hamiltonian systems on $\mathbb C\times(\mathbb C\setminus\{0\})$ with standard symplectic structure $\omega_{\mathbb C}=dz\wedge dw$ and Hamiltonian function $f=a z^2+b/w+P_n(w)$, where $P_n(w)$ is a polynomial of degree $n$, the numbers $a,b\in\mathbb C$ and $ab\ne0$. For some natural classes of these $\mathbb C$-Hamiltonian systems we study an equivalence relation in the Hamiltonian sense and determine the topology of the corresponding quotient space. We also prove that for $\mathbb C$-Hamiltonian systems with Hamiltonian function $f=a z^2+b/w+P_n(w)$, where $a b\ne0,n\ge0$, the bifurcation complex is homeomorphic to a two-dimensional plane.

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