  We show that anisotropic Bianchi type-IX models, with matter and cosmological
constant have chaotic dynamics, connected to the presence of a saddle-center in
phase space. The topology of cylinders emanating from unstable periodic orbits
about the saddle-center provides an invariant characterization of chaos in the
models. The model can be thought to describe the early stages of inflation, the
way out to inflation being chaotic.
