| Contents |
| Oscillatory motions in the three body problem or its simplified
versions, the different instances of the restricted three body
problem, R3BP, are solutions such that two of the bodies, the
primaries, evolve describing bounded orbits while the third one
moves closer and closer to infinity, but always returning to a fixed
neighborhood of the primaries. They are one of the seven types of
possible orbits in the three body problem, according to Chazy (four
in the case of the R3BP), who knew examples of orbits of the other
six types, but not of oscillatory ones.
The existence of oscillatory orbits has been proved in several
instances of the R3BP by several authors, Sitnikov, Alexeev, Moser,
Llibre and Sim\'{o}, Moeckel, among others.
In this work we first address the existence of oscillatory motions
in the restricted planar circular three body problem, and we prove
that they exist for all values of the masses of the primaries, thus
closing the problem in this case.
Next, in the planar three body problem with arbitrary masses, we
consider the case when two of the masses evolve in bounded orbits
close to elliptic motions with small eccentricity while the third
one performs oscillatory motion. |
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