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The dynamics of a general Bianchi IX model with three scale factors isexamined. The matter content of the model is assumed to be comoving dust plus apositive cosmological constant. The model presents a critical point ofsaddle-center-center type in the finite region of phase space. This criticalpoint engenders in the phase space dynamics the topology of stable and unstablefour dimensional tubes $R \times S^3$, where $R$ is a saddle direction and$S^3$ is the manifold of unstable periodic orbits in the center-center sector.A general characteristic of the dynamical flow is an oscillatory mode aboutorbits of an invariant plane of the dynamics which contains the critical pointand a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair oftubes (one stable, one unstable) emerging from the neighborhood of the criticalpoint towards the FRW singularity have homoclinic transversal crossings. Thehomoclinic intersection manifold has topology $R \times S^2$ and is constitutedof homoclinic orbits which are bi-asymptotic to the $S^3$ center-centermanifold. This is an invariant signature of chaos in the model, and produceschaotic sets in phase space. The model also presents an asymptotic DeSitterattractor at infinity and initial conditions sets are shown to have fractalbasin boundaries connected to the escape into the DeSitter configuration(escape into inflation), characterizing the critical point as a chaoticscatterer.Comment: 11 pages, 6 ps figures. Accepted for publication in Phys. Rev.

Homoclinic chaos in the dynamics of a general Bianchi type-IX model