Remark on bouncing and cyclic branes in more than one extra dimension

We argue that bouncing branes occur naturally when there is more than one extra dimension. We consider three-branes embedded in space-times with a horizon and an isometry group SO(6). As soon as the brane angular momentum is large enough, a repulsive barrier prevents the branes from reaching the horizon. We illustrate this phenomenon with the case of D3-branes in an AdS(5)-Schwarzschild x S-5 background and asymptotically flat space-time.