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.