The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows

Details The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows The Liouville-type theorem for integrable Hamiltonian systems with incomplete flows

2012-03-24

arxiv.org/abs/1203.5455v1

Mathematics

Differential Geometry

6 pages

Scientific paper

For integrable Hamiltonian systems with two degrees of freedom whose Hamiltonian vector fields have incomplete flows, an analogue of the Liouville theorem is established. A canonical Liouville fibration is defined by means of an "exact" 2-parameter family of flat polygons equipped with certain pairing of sides. For the integrable Hamiltonian systems given by the vector field $v=(-\partial f/\partial w, \partial f/\partial z)$ on ${\mathbb C}^2$ where $f=f(z,w)$ is a complex polynomial in 2 variables, geometric properties of Liouville fibrations are described.

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