Luca Sbano, SISSA/ISAS Trieste Italia; e-mail sbano@tsmi19.sissa.it
On the lack of coercivity of the reduced Action-functional for
zero total angular momentum in the planar
Newtonian three-body problem
(57K, LAtex)
ABSTRACT. Combining hamiltonian reduction, variational methods and local analysis of the
flow, we study for the planar three-body problem, the existence
of non trivial periodic orbit without collisions,
with zero total angular momentum.
We prove that collision solutions are not minima, but the lack
of compactness for the sub-levels
of the Action-functional does not allow to prove
the existence of $T$-periodic orbits without collisions. We restrict therefore
to study periodic solutions which are odd under reflection (thorough some axis
which may depend on the orbit). In this setting we prove that the loss
of compactness is due to trajectories which are asymptotically collinear
and we identify a class of sets which are compact and which are good
candidates for the search of a minimum.
(In the fonts there are some AMStex fonts)