Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entire minimal parabolic trajectories: the planar anisotropic Kepler
  problem   We continue the variational approach to parabolic trajectories introduced in
our previous paper [5], 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 trajectories 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.

12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex