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)