  In a non-compact context the first natural step in the search for periodic
orbits of a hamiltonian flow is to detect bounded ones. In this paper we show
that, in a non-compact setting, certain algebraic topological constraints
imposed to a gradient flow of the hamiltonian function $f$ imply the existence
of bounded orbits for the hamiltonian flow of $f$. Once the existence of
bounded orbits is established, under favorable circumstances, application of
the $C^{1}$-closing lemma leads to periodic ones.
