Adiabatic invariants and Mixmaster catastrophes

Abstract

We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical results. We also present a new formulation of the dynamics via Catastrophe Theory. We find that the change from one era to the next corresponds to a fold catastrophe, during the Kasner shifts the potential is an Implicit Function Form whereas, as the anisotropy dissipates, the Mixmaster potential must become a Morse 0--saddle. We compare and contrast our results to many known works on the Mixmaster problem and indicate how extensions could be achieved. Further exploitation of this formulation may lead to a clearer understanding of the global Mixmaster dynamics.

24 pages, LaTeX, 5 figures (which can be obtained by sending a message to the first author), submitted to Phys.Rev.D

References in corpus (2)

• The Bianchi Ix (MIXMASTER) Cosmological Model is Not Integrable
• The Mixmaster Spacetime, Geroch's Transformation and Constants of Motion

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