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

Abstract

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.

6 pages

References in corpus (1)

• Connected components of the moduli spaces of Abelian differentials with prescribed singularities

Cited by in corpus (3)

• Symplectic invariants for parabolic orbits and cusp singularities of integrable systems with two degrees of freedom
• Hidden toric symmetry and structural stability of singularities in integrable systems
• Structurally stable non-degenerate singularities of integrable systems