  In a previous paper [3] we have studied flows on polytopes presenting a
method to encapsulate its asymptotic dynamics along the heteroclinic network
formed by the polytope's edges and vertices. These results apply to the class
of polymatrix replicator systems, which contains several important models in
Evolutionary Game Theory. Here we establish the Hamiltonian character of the
asymptotic dynamics of Hamiltonian polymatrix replicators.
