  We demonstrate how an effective density of states can be derived from the
S-matrix describing a coupled-channel system. Besides the locations of poles,
the phase of the determinant of the S-matrix encodes essential details in
characterizing the dynamics of resonant and non-resonant interactions. The
density of states is computed for the two channel scattering problem ($\pi\pi,
K \bar{K}$, S-wave), and the influences from the various dynamical structures:
poles, roots, branch cuts, and Riemann sheets, are examined.
