## ABSTRACT

Chapter 6

Classication of Hamiltonian Flows

on Two-Dimensional Surfaces

up to Topological Conjugacy

6.1. INVARIANTS OF A HAMILTONIAN

SYSTEM ON A 2-ATOM

In this section we produce a complete set of invariants giving the classication

of Hamiltonian systems with one degree of freedom in a neighborhood of a singular

level of the Hamiltonian up to topological conjugacy. When we speak of topological

conjugacy of such systems, we mean the existence of a homeomorphism that not only

conjugates ows, but also preserves orientation.