ADIABATIC INVARIANTS AND MIXMASTER CATASTROPHES

We present a rigorous analysis of the role and uses of the adiabatic i nvariant in the mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behavi or over the commonly used one. We illustrate its behavior in a number of numerical results. We also present a new formulation of the dynamic s via catastrophe theory. We find that the change from one era to the next corresponds to a fold catastrophe, during the Kasner shifts the p otential is an implicit function form whereas, as the anisotropy dissi pates, the mixmaster potential must become a Morse O-saddle. We compar e and contrast our results to many known works on the mixmaster proble m and indicate how extensions could be achieved. Further exploitation of this formulation may lead to a clearer understanding of the global mixmaster dynamics.