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      The mixmaster universe: A chaotic Farey tale

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          Abstract

          When gravitational fields are at their strongest, the evolution of spacetime is thought to be highly erratic. Over the past decade debate has raged over whether this evolution can be classified as chaotic. The debate has centered on the homogeneous but anisotropic mixmaster universe. A definite resolution has been lacking as the techniques used to study the mixmaster dynamics yield observer dependent answers. Here we resolve the conflict by using observer independent, fractal methods. We prove the mixmaster universe is chaotic by exposing the fractal strange repellor that characterizes the dynamics. The repellor is laid bare in both the 6-dimensional minisuperspace of the full Einstein equations, and in a 2-dimensional discretisation of the dynamics. The chaos is encoded in a special set of numbers that form the irrational Farey tree. We quantify the chaos by calculating the strange repellor's Lyapunov dimension, topological entropy and multifractal dimensions. As all of these quantities are coordinate, or gauge independent, there is no longer any ambiguity--the mixmaster universe is indeed chaotic.

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          Most cited references 39

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          General Relativity

           Robert Wald (1984)
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            Oscillatory approach to a singular point in the relativistic cosmology

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              Mixmaster Universe

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                Author and article information

                Journal
                30 December 1996
                10.1103/PhysRevD.55.7489
                gr-qc/9612066
                Custom metadata
                CfPA-96-TH-17
                Phys.Rev. D55 (1997) 7489-7510
                45 pages, RevTeX, 19 Figures included, submitted to PRD
                gr-qc chao-dyn nlin.CD

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