We introduce a class of Hamiltonian scattering systems which can be reduced to the "normal form" P = 0, Q = P, by means of a global canonical transformation (P, Q) = A( p, q), p, q in R^n, defined through asymptotic properties of the trajectories. These systems are obtained requiring certain geometrical conditions on p = -V'(q), q' = p, where V is a bounded below "cone porential", i.e., the force -V'(q) always belongs to a closed convex cone which contains no straight lines. We can deal with very different asymptotic behaviours of the potential and the potential can undergo small perturbations in any arbitrary compact set without losing the existence and the properties of A.
Reducing scattering problems under cone potential to normal form by global canonical transformations.
GORNI, Gianluca;
1990-01-01
Abstract
We introduce a class of Hamiltonian scattering systems which can be reduced to the "normal form" P = 0, Q = P, by means of a global canonical transformation (P, Q) = A( p, q), p, q in R^n, defined through asymptotic properties of the trajectories. These systems are obtained requiring certain geometrical conditions on p = -V'(q), q' = p, where V is a bounded below "cone porential", i.e., the force -V'(q) always belongs to a closed convex cone which contains no straight lines. We can deal with very different asymptotic behaviours of the potential and the potential can undergo small perturbations in any arbitrary compact set without losing the existence and the properties of A.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
