Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles

Understand

We consider cosmological models of Bianchi type.

• In particular, we are interested in the alpha-limit dynamics near the Kasner circle of equilibria for Bianchi classes VIII and IX.
• They correspond to cosmological models close to the big-bang singularity.
• We prove the existence of a codimension-one family of solutions that limit, for t to negative infinity, onto a heteroclinic 3-cycle to the Kasner circle of equilibria.