  The excitation spectra of the T=0 dynamic structure factors for the spin,
dimer, and trimer fluctuation operators as well as for the newly defined center
fluctuation operator in the one-dimensional S=1 Heisenberg model wi th
isotropic bilinear $(J\cos\theta)$ and biquadratic $(J\sin\theta)$ exchange are
investigated via the recursion method for systems with up to N=18 site s over
the predicted range, $-\pi/4<\theta\lesssim\pi/4$, of the topologically ordered
Haldane phase. The four static and dynamic structure factors probe t he
ordering tendencies in the various coupling regimes and the elementary and
composite excitations which dominate the T=0 dynamics. At $\theta =
\arctan{1/3}$ (VBS point), the dynamically relevant spectra in the invariant
subspaces with total spin $S_T = 0,1,2$ are dominated by a branch of magnon
states $(S_T = 1)$, by continua of two-magnon scattering states $(S_T =
0,1,2)$, and by discrete branches of two-magnon bound states with positive
interaction energy $(S_T = 0,2)$. The dimer and trimer spectra at $q=\pi$ ar e
found to consist of single modes with $N$-independent excitation energies
$\omega_\lambda^D/|e_0|=5$ and $\omega_\lambda^T/|e_0|=6$, where $e_0=E_0/N$ is
the ground-state energy per site. The basic structure of the dynamically
relevant excitation spectrum remains the same over a substantial parameter
range within the Haldane phase. At the transition to the dimerized phase
($\theta=-\pi/4$), the two-magnon excitations turn into two-spinon excitations.
