  We study the dynamics and thermodynamics of a probe D3-brane in the rotating
D3-brane background and in its extremal limit, which is a multicenter
configuration of D3-branes distributed uniformly on a disc. In the extremal
background, if the angular momentum of the probe does not vanish, the probe is
always bounced back at some turning point. When its angular momentum vanishes,
in the disc plane, the probe will be captured at the edge of the disc; in the
hyperplane orthogonal to the disc, the probe will be absorbed at the center of
the disc. In the non-extremal background, if the probe is in the hyperplane
orthogonal to the disc, it will be captured at the horizon; if the probe is
restricted in the disc plane, the probe will be bounced back at a turning
point, which is just the infinite red-shift hyperplane of the rotating
background, even when the angular momentum of the probe vanishes. The
thermodynamics of a relative static D3-brane probe is also investigated to the
rotating D3-brane source. Two critical points are found. One is just the
thermodynamically stable boundary of the source rotating D3-branes; the other
is related to the distance between the probe and the source, which can be
regarded as the mass scale in the corresponding super Yang-Mills theory. If the
probe is static, the second critical point occurs as the probe is at the
infinite red-shift hyperplane of the background. The relevance to the
thermodynamics of the super Yang-Mills theory is discussed briefly.
