## 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

.