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We consider cosmological models with a scalar field with equation of state$w\ge 1$ that contract towards a big crunch singularity, as in recent cyclicand ekpyrotic scenarios. We show that chaotic mixmaster oscillations due toanisotropy and curvature are suppressed, and the contraction is described by ahomogeneous and isotropic Friedmann equation if $w>1$. We generalize theresults to theories where the scalar field couples to p-forms and show thatthere exists a finite value of $w$, depending on the p-forms, such that chaoticoscillations are suppressed. We show that $Z_2$ orbifold compactification alsocontributes to suppressing chaotic behavior. In particular, chaos is avoided incontracting heterotic M-theory models if $w>1$ at the crunch.Comment: 25 pages, 2 figures, minor changes, references adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Kasner and mixmaster behavior in universes with equation of state<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>w</mml:mi><mml:mo>&gt;~</mml:mo><mml:mn>1</mml:mn></mml:math>

Kasner and mixmaster behavior in universes with equation of statew>~1