The Poincare Map in the Regular Neighbourhoods of the Liouville Critical Leaves of an Integrable Hamiltonian System
1997, Volume 2, Number 2, pp. 79-86
Author(s): Topalov P. I.
Author(s): Topalov P. I.
In this paper we investigate the Poincare map in the regular neighbourhood of a critical leaf of the Liouville foliation of an integrable Hamiltonian system with two degrees of freedom. It was proved in [3], that for an arbitrary surface transversal to the trajectories, the Poincare map is a one-time-map along the flow of some Hamiltonian, which is defined on the considering surface (this Hamiltonian is called "the Poincare Hamiltonian"). In the paper [4] it was proved that for every transversal surface the Poincare map is a restriction to the surface of some smooth function, which is defined on the regular neighbourhood of the critical leaf.
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