ABSTRACT
Chapter 9
Liouville Classication of Integrable
Systems with Two Degrees of Freedom
in Four-Dimensional Neighborhoods
of Singular Points
In this chapter, we present the results obtained by L. M. Lerman, Ya. L. Umanski
[212], [213], A. V. Bolsinov [44], V. S. Matveev [220], [221], Nguyen Tien Zung
[258], [261]. We shall follow the general idea of our book: try to present all facts from
the uniform viewpoint of the theory of topological invariants of integrable systems.
The preceding chapters were devoted to studying an integrable Hamiltonian system
on a three-dimensional isoenergy manifold. Here we wish to discuss its behavior
on a four-dimensional symplectic manifold. We shall mainly be interested in
the topological structure of the corresponding Liouville foliation.
