Abstract
We construct the most general form of axially symmetric SU(2) - Yang - Mills fields in Bianchi cosmologies. The dynamical evolution of axially symmetric Yang - Mills fields in the Bianchi I model is compared with the dynamical evolution of the electromagnetic field in Bianchi I and the fully isotropic Yang - Mills field in Friedmann - Robertson - Walker cosmologies. The stochastic properties of axially symmetric Bianchi I - Einstein - Yang - Mills systems are compared with those of axially symmetric Yang - Mills fields in flat space. After numerical computation of Liapunov exponents in synchronous (cosmological) time, it is shown that the Bianchi I - Einstein - Yang - Mills system has milder stochastic properties than the corresponding flat Yang - Mills system. The Liapunov exponent is non-vanishing in conformal time.
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