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We introduce a class of Hamiltonian scattering systems which can be reducedto the "normal form" $\dot P=0$, $\dot Q=P$, by means of a global canonicaltransformation $ (P,Q)=A(p,q), p,q\in R^n$, defined through asymptoticproperties of the trajectories.  These systems are obtained requiring certain geometrical conditions on $\dotp=-\nabla V(q)$, $\dot q=p$, where $V$ is a bounded below "cone potential",i.e., the force $-\nabla V(q)$ always belongs to a closed convex cone whichcontains no straight lines.  We can deal with very different asymptotic behaviours of the potential andthe potential can undergo small perturbations in any arbitrary compact setwithout losing the existence and the properties of $A$.

Reducing scattering problems under cone potentials to normal form by global canonical transformations