Entire Parabolic Trajectories as Minimal Phase Transitions

Details Entire Parabolic Trajectories as Minimal Phase Transitions Entire Parabolic Trajectories as Minimal Phase Transitions

2011-05-17

arxiv.org/abs/1105.3358v1

Mathematics

Dynamical Systems

44 pages, 7 figures

Scientific paper

For the class of anisotropic Kepler problems in $\RR^d\setminus\{0\}$ 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 codimension-one submanifold of such potentials. We give them a variational characterization in terms of the behavior of the parameter-free minimizers of an associated obstacle problem. We then give a full characterization of such a codimension-one manifold of potentials and we show how to parameterize it with respect to the degree of homogeneity.

Affiliated with

Also associated with

No associations

Rating

Entire Parabolic Trajectories as Minimal Phase Transitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Entire Parabolic Trajectories as Minimal Phase Transitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entire Parabolic Trajectories as Minimal Phase Transitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727759