ABSTRACT
Chapter 4
Liouville Equivalence of Integrable
Systems with Two Degrees of Freedom
Now we make more precise the denition of the Liouville equivalence for integrable
Hamiltonian systems. From now on, we shall assume that two Liouville foliations
are Liouville equivalent if and only if there exists a dieomorphism that sends
the leaves of the rst foliation to those of the second one and satises two conditions
related to the orientation. Namely, it preserves the orientation on 3-manifolds
Q and Q
, and moreover, it also preserves the orientation on the critical circles
given by the Hamiltonian ows.
