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arXiv · 0907.0653

Monotonic functions in Bianchi models: Why they exist and how to find them

J. Mark Heinzle·Claes Uggla
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Abstract

All rigorous and detailed dynamical results in Bianchi cosmology rest upon the existence of a hierarchical structure of conserved quantities and monotonic functions. In this paper we uncover the underlying general mechanism and derive this hierarchical structure from the scale-automorphism group for an illustrative example, vacuum and diagonal class A perfect fluid models. First, kinematically, the scale-automorphism group leads to a reduced dynamical system that consists of a hierarchy of scale-automorphism invariant sets. Second, we show that, dynamically, the scale-automorphism group results in scale-automorphism invariant monotone functions and conserved quantities that restrict the flow of the reduced dynamical system.

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J. Mark Heinzle, Claes Uggla. 2009-12-01. Monotonic functions in Bianchi models: Why they exist and how to find them. https://doi.org/10.1088/0264-9381%2F27%2F1%2F015009

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