|Titolo||Entire minimal parabolic trajectories: the planar anisotropic Kepler problem|
|Autore/i||Barutello, V.; Terracini, S.; Verzini, G.|
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|Abstract||We continue the variational approach to parabolic tra jectories introduced in our previous paper , which sees parabolic orbits as minimal phase transitions.
We deepen and complete the analysis in the planar case for homogeneous singular potentials. We characterize all parabolic orbits connecting two minimal central conﬁgurations as free-time Morse minimizers (in a given homotopy class of paths). These may occur for at most one value of the homogeneity exponent. In addition, we link this threshold of existence of parabolic tra jectories with the absence of collisions for all the
minimizers of ﬁxed-ends problems. Also the existence of action minimizing periodic trajectories with nontrivial homotopy type can be related with the same threshold.|