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We use the Fuchsian algorithm to study the behavior near the singularity ofcertain families of U(1) Symmetric solutions of the vacuum Einstein equations(with the U(1) isometry group acting spatially). We consider an analytic familyof polarized solutions with the maximum number of arbitrary functionsconsistent with the polarization condition (one of the ``gravitational degreesof freedom'' is turned off) and show that all members of this family areasymptotically velocity term dominated (AVTD) as one approaches thesingularity. We show that the same AVTD behavior holds for a family of ``halfpolarized'' solutions, which is defined by adding one extra arbitrary functionto those characterizing the polarized solutions. (The full set of non-polarizedsolutions involves two extra arbitrary functions). We begin to address theissue of whether AVTD behavior is independent of the choice of time foliationby showing that indeed AVTD behavior is seen for a wide class of choices ofharmonic time in the polarized and half-polarized (U(1) Symmetric vacuum)solutions discussed here. \Comment: 42 pge

Asymptotic behaviour in polarized and half-polarized U (1) symmetric vacuum spacetimes