Codice  QDD 100 
Titolo  Entire Parabolic Trajectories as Minimal Phase Transitions 
Data  20110530 
Autore/i  Barutello, V.; Terracini, S.; Verzini, G. 
Link  Download full text 
Abstract  For the class of anisotropic Kepler problems in any spatial dimension, with homogeneous potentials, we seek parabolic trajectories having prescribed asymptotic directions at infinity and which, in addition, are Morse minimizing geodesics for the Jacobi metric. Such trajectories correspond to saddle heteroclinics on the collision manifold, are structurally unstable and appear only for a codimensionone submanifold of such potentials. We give them a variational characterization in terms of the behavior of the parameterfree minimizers of an associated obstacle problem. We then give a full characterization of such a codimensionone manifold of potentials and we show how to parameterize it with respect to the degree of homogeneity. 
