  We consider the planar restricted $N$-body problem where the $N-1$ primaries
are assumed to be in a central configuration whereas the infinitesimal particle
escapes to infinity in a parabolic orbit. We prove the existence of transversal
intersections between the stable and unstable manifolds of the parabolic orbits
at infinity which guarantee the existence of a Smale's horseshoe. This implies
the occurrence of chaotic motions but also of oscillatory motions, that is,
orbits for which the massless particle leaves every bounded region but it
returns infinitely often to some fixed bounded region. Our achievement is based
in an adequate scaling of the variables which allows us to write the
Hamiltonian function as the Hamiltonian of the Kepler problem multiplied by a
small quantity plus higher-order terms that depend on the chosen configuration.
We compute the Melnikov function related to the first two non-null perturbative
terms and characterize the cases where it has simple zeroes. Concretely, for
some combinations of the configuration parameters, i.e. mass values and
positions of the primaries, the Melnikov function vanishes, otherwise it has
simple zeroes and the transversality condition is satisfied. The theory is
illustrated for various cases of restricted $N$-body problems, including the
circular restricted three-body problem. No restrictions on the mass parameters
are assumed.
