Signature for local Mixmaster dynamics in U(1) symmetric cosmologies

Previous studies \cite{berger98a} have provided strong support for a local, oscillatory approach to the singularity in U(1) symmetric, spatially inhomogeneous vacuum cosmologies on $T^3 \times R$. The description of a vacuum Bianchi type IX, spatially homogeneous Mixmaster cosmology (on $S^3 \times R$) in terms of the variables used to describe the U(1) symmetric cosmologies indicates that the oscillations in the latter are in fact those of local Mixmaster dynamics. One of the variables of the U(1) symmetric models increases only at the end of a Mixmaster era. Such an increase therefore yields a qualitative signature for local Mixmaster dynamics in spatially inhomogeneous cosmologies.