ABSTRACT
Rough Liouville Equivalence
of Integrable Systems with
Two Degrees of Freedom
3.1. CLASSIFICATION OF NON-DEGENERATE
CRITICAL SUBMANIFOLDS ON ISOENERGY
3-SURFACES
Consider a symplectic manifold M
with an integrable Hamiltonian system
v = sgradH ; let Q
h
be a non-singular compact connected isoenergy 3-surface
in M
. Let f be an additional integral of the system v that is independent
of H . We denote its restriction to Q
h
by the same letter f . Recall that f is
assumed to be a Bott function on Q
h
. Our aim is to investigate the topology
of the Liouville foliation on Q
h
dened by the given integrable system. Its non-
singular leaves are Liouville tori, and the singular ones correspond to critical levels
of the integral f on Q
h
.
