The cosmological billiard attractor

• DOI: 10.4310/atmp.2009.v13.n2.a1
• Publication Date: 2013-08-30T21:01:56Z
• Authors: J. Mark Heinzle; Niklas Röhr; Claes Uggla
• Keywords: Dynamical billiards; Friedmann–Lemaître–Robertson–Walker metric

This article is devoted to a study of the asymptotic dynamics generic solutions Einstein vacuum equations toward spacelike singularity.Starting from fundamental assumptions about nature singularities, we derive in step-by-step manner cosmological billiard conjecture: show that represented by (randomized) sequences heteroclinic orbits on "billiard attractor".Our analysis rests two pillars: (i) dynamical systems formulation based conformal Hubblenormalized orthonormal frame approach expressed an Iwasawa frame; (ii) stochastic methods and interplay between genericity stochasticity.Our work generalizes improves level rigor previous Belinskii, Khalatnikov, Lifshitz; furthermore, establish our Hamiltonian "cosmological billiards", as elaborated Damour, Hennaux, Nicolai, can be viewed yielding "dual" representations dynamics.