We consider cosmological models with a scalar field with equation of state w \geq 1 that contract towards a big crunch singularity , as in recent cyclic and ekpyrotic scenarios .
We show that chaotic mixmaster oscillations due to anisotropy and curvature are suppressed , and the contraction is described by a homogeneous and isotropic Friedmann equation if w > 1 .
We generalize the results to theories where the scalar field couples to p –forms and show that there exists a finite value of w , depending on the p –forms , such that chaotic oscillations are suppressed .
We show that \mathbb { Z } _ { 2 } orbifold compactification also contributes to suppressing chaotic behavior .
In particular , chaos is avoided in contracting heterotic M -theory models if w > 1 at the crunch .