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The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of two other bodies, the primaries, which evolve in Keplerian ellipses.

A trajectory is called oscillatory if it leaves every bounded region but returns infinitely often to some fixed bounded region. We prove the existence of such type of trajectories for any values for the masses of the primaries provided the eccentricity of the Keplerian ellipses is small.

We study the Gevrey character of a natural parameterization of one dimensional invariant manifolds associated to a *parabolic direction* of fixed points of analytic maps, that is, a direction associated with an eigenvalue equal to 1. We show that, under general hypotheses, these invariant manifolds are Gevrey with type related to some explicit constants. We provide examples of the optimality of our results as well as some applications to celestial mechanics, namely, the Sitnikov problem and the restricted planar three body problem.

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