We use a set of high-resolution N-body simulations of the Galactic disk to study its interactions with the population of satellites predicted cosmologically. One simulation illustrates that multiple passages of massive satellites with different velocities through the disk generate a wobble, having the appearance of rings in face-on projections of the stellar disk. They also produce flares in the disk outer parts and gradually heat the disk through bending waves. A different numerical experiment shows that an individual satellite as massive as the Sagittarius dwarf galaxy passing through the disk will drive coupled horizontal and vertical oscillations of stars in underdense regions, with small significant associated heating. This experiment shows that vertical excursions of stars in these low-density regions can exceed 1 kpc in the Solar neighborhood, resembling the coherent vertical oscillations recently detected locally. They can also induce non-zero vertical streaming motions as large as 10-20 km s$^{-1}$, consistent with recent observations in the Galactic disk. This phenomenon appears as a local ring, with modest associated disk heating.
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