  We investigate the phase diagram of a spin--1 Ising spin-glass model on a
Cayley tree. According to early work of Thompson and collaborators, this
problem can be formulated in terms of a set of nonlinear discrete recursion
relations along the branches of the tree. Physically relevant solutions
correspond to the attractors of these mapping equations. In the limit of
infinite coordination of the tree, and for some choices of the model
parameters, we make contact with findings for the phase diagram of more
recently investigated versions of the Blume-Emery-Griffiths spin-glass model.
In addition to the anticipated phases, we numerically characterize the
existence of modulated and chaotic structures.
