  To systematically analyze the dynamical implications of the matter content in
cosmology, we generalize earlier dynamical systems approaches so that perfect
fluids with a general barotropic equation of state can be treated. We focus on
locally rotationally symmetric Bianchi type IX and Kantowski-Sachs orthogonal
perfect fluid models, since such models exhibit a particularly rich dynamical
structure and also illustrate typical features of more general cases. For these
models, we recast Einstein's field equations into a regular system on a compact
state space, which is the basis for our analysis. We prove that models expand
from a singularity and recollapse to a singularity when the perfect fluid
satisfies the strong energy condition. When the matter source admits Einstein's
static model, we present a comprehensive dynamical description, which includes
asymptotic behavior, of models in the neighborhood of the Einstein model; these
results make earlier claims about ``homoclinic phenomena and chaos'' highly
questionable. We also discuss aspects of the global asymptotic dynamics, in
particular, we give criteria for the collapse to a singularity, and we describe
when models expand forever to a state of infinite dilution; possible initial
and final states are analyzed. Numerical investigations complement the
analytical results.
