  Using six-dimesional phase-space information from the Fourth Data release of
the Radial Velocity Experiment (RAVE) over the range of Galactic longitude
240$^{\circ}< l <$ 360$^{\circ}$ and $V_{LSR} < -239$ kms$^{-1}$, we have
computed orbits for 329 RAVE stars that were originally selected as chemically
and kinematically related to $\omega$ Centauri. The orbits were integrated in a
Milky-Way-like axisymmetric Galactic potential, ignoring the effects of the
dynamical evolution of $\omega$ Centauri due to the tidal effects of the Galaxy
disk on the cluster along time. We also ignored secular changes in the Milky
Way potential over time. In a Monte Carlo scheme, and under the assumption that
the stars may have been ejected with velocities greater than the escape
velocity ($V_{rel}>V_{esc,0}$) from the cluster, we identified 15 stars as
having close encounters with $\omega$ Centauri: (\textit{i}) 8 stars with
relative velocities $V_{rel}< 200 $ kms$^{-1}$ may have been ejected $\sim$ 200
Myr ago from $\omega$ Centauri; (\textit{ii}) other group of 7 stars were
identified with high relative velocity $V_{rel}> 200 $ kms$^{-1}$ during close
encounters, and seems unlikely that they have been ejected from $\omega$
Centauri. We also confirm the link between J131340.4-484714 as potential member
of $\omega$ Centauri, and probably ejected $\sim$ 2.0 Myr ago, with a relative
velocity $V_{rel}\sim80$ kms$^{-1}$.
