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abstract: 'Confirming previous heuristic analyses à la Belinskii-Khalatnikov-Lifshitz, it is rigorously proven that certain “subcritical” Einstein-matter systems exhibit a monotone, generalized Kasner behaviour in the vicinity of a spacelike singularity. The $D-$dimensional coupled Einstein-dilaton-$p$-form system is subcritical if the dilaton couplings of the $p$-forms belong to some dimension dependent open neighbourhood of zero [@dh1], while pure gravity is subcritical if $D \geq 11$ [@DHS]. Our proof relies, like the recent theorem [@AR] dealing with the (always subcritical [@BK2]) Einstein-dilaton system, on the use of Fuchsian techniques, which enable one to construct local, analytic solutions to the full set of equations of motion. The solutions constructed are “general” in the sense that they depend on the maximal expected number of free functions.'
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IHES/P/02/06\
ULB-TH-02/01

1.0cm

[Thibault Damour$^{a}$, Marc Henneaux$^{b,c}$, Alan D. Rendall$^{d}$ and\
Marsha Weaver$^{b}$]{}\
$^a$ Institut des Hautes Etudes Scientifiques, 35, Route de Chartres, F-91440 Bures-sur-Yvette, France\
$^b$ Physique Théorique et Mathématique, Université Libre de Bruxelles, C.P. 231, B-1050, Bruxelles, Belgium\
$^c$ Centro de Estudios Científicos, Casilla 1469, Valdivia, Chile\

$^d $Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany

Introduction
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The problem
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In recent papers [@dh1; @dh2; @tDmH], the dynamics of the coupled Einstein-dilaton-$p$-form 