  We study the dynamics of anisotropic Bianchi type-IX models with matter and
cosmological constant. The models can be thought as describing the role of
anisotropy in the early stages of inflation. The concurrence of the
cosmological constant and anisotropy are sufficient to produce a chaotic
dynamics in the gravitational degrees of freedom, connected to the presence of
a critical point of saddle-center type in the phase space of the system. The
invariant character of chaos is guaranteed by the topology of the cylinders
emanating from unstable periodic orbits in the neighborhood of the
saddle-center. We discuss a possible mechanism for amplification of specific
wavelengths of inhomogeneous fluctuations in the models. A geometrical
interpretation is given for Wald's inequality in terms of invariant tori and
their destruction by increasing values of the cosmological constant.
